Mensuration-iii (surface Area And Volume Of A Right Circular Cylinder
Class 8th Mathematics RD Sharma Solution
- Find the curved surface area dna total surface area of a cylinder, the diameter…
- The curved surface area of a cylindrical road is 132 cm^2 . Find its length if…
- The area of the base of a right circular cylinder is 616 cm^2 and its height is…
- The circumference of the base of a cylinder is 88 cm and its height is 15 cm.…
- A rectangular strip 25 cm 7 cm is rotated about the longer side. Find the total…
- A rectangular sheet of paper, 44 cm 20 cm, is rolled along its length to form a…
- The radii of two cylinders are in the ratio 2 : 3 and their heights are in the…
- The ratio between the curved surface area and the total surface area of a right…
- The curved surface area of a cylinder is 1320 cm^2 and its base has diameter 21…
- The height of a right circular cylinder is 10.5 cm. If three times the sum of…
- Find the cost of plastering the inner surface of a well at Rs. 9.50 per m^2 ,…
- A cylindrical vessel open at the top has diameter 20 cm and height 14 cm. Find…
- The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find the cost…
- The diameter of a roller is 84 cm and its length is 120 cm. It takes 500…
- Twenty one cylindrical pillars of the Parliament House are to be cleaned. If…
- The total surface area of a hollow cylinder which is open from both sides if…
- The sum of the radius of the base and height of a solid cylinder is 37 m. If…
- Find the ratio between the total surface area of a cylinder to its curved…
- A cylindrical vessel, without lid, has to be tin-coated on its both sides. If…
- Find the volume of a cylinder whose (i) r = 3.5 cm, h = 40 cm (ii) r = 2.8 m, h…
- Find the volume of a cylinder, if the diameter (d) of its base and its altitude…
- The area of the base of a right circular cylinder is 616 cm^2 and its height is…
- The circumference of the base of a cylinder is 88 cm and its height is 15 cm.…
- A hollow cylindrical pipe is 21 dm long. Its outr and inner diameters are 10 cm…
- Find the (i) curved surface area (ii) total surface area and (iii) volume of a…
- The diameter of the base of a right circular cylinder is 42 cm and its height…
- Find the volume of cylinder, the diameter of whose base is 7 cm and height…
- A rectangular strip 25 cm 7 cm is rotated about the longer side. Find the…
- A rectangular sheet of paper, 44 cm 20 cm, is rolled along its length to form…
- The volume and the curved surface area of cylinder are 1650 cm^3 and 660 cm^2…
- The radii of two cylinders are in the ratio 2 : 3 and their heights are in the…
- The ratio between the curved surface area dna the total surface area of a…
- The curved surface area of a cylinder is 1320 cm^2 and its base has diameter…
- The ratio between the radius of the base and the height jof a cylinder is 2 :…
- The curved surface area of a cylindrical pillar is 264 m^2 and its volume is…
- Two circular cylinders of equal volumes have their heights in the ratio 1 : 2.…
- The height of a right circular cylinder is 10/5 m. Three times the sum of the…
- How many cubic metres of earth must be dug-out to sink a well 21 m deep and 6…
- The trunk of a tree is cylindrical and its circumference is 176 cm. If the…
- A well is dug 20 m deep and it has a diameter of 7 m. The earth which is so…
- A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been…
- A cylindrical container with diameter of base 56 cm contains sufficient water…
- A rectangular sheet of paper 30 cm 18 cm can be transformed into the curved…
- The rain which falls on a roof 18 m long and 16.5 m wide is allowed to be…
- A piece of ductile metal is in the form of a cylinder of diameter 1 cm and…
- Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of…
- 2.2 cubic dm of brass is to be drawn into cylindrical wire 0.25 cm in…
- The difference between inside and outside surfaces of a cylindrical tube 14 cm…
- Water flows out through a circular pipe whose internal diameter is 2 cm, at…
- A cylindrical tube, open at both ends, is made of metal. The internal diameter…
- From a tap of inner radius 0.75 cm, water flows at the rate of 7 m per second.…
- A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a…
- A rectangular sheet of paper 30 cm 18 cm be transformed into the curved…
- How many litres of water flows out of a pipe having an area of cross section…
- A solid cylinder has a total surface area of 231 cm^2 . It curved surface area…
- Find the cost of sinking a tube well 280 m deep, having diameter 3 m at the…
- Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of…
- 2.2 cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in…
- A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is…
- A hollow garden roller, 63 cm wide with a girth of 440 cm, is made of 4 cm…
- What length of a solid cylinder 2 cm in diameter must be taken to recast into…
- In the middle of a rectangular field measuring 30m 20m, a well of 7 m diameter…
Exercise 22.1
Question 1.Find the curved surface area dna total surface area of a cylinder, the diameter of whose base is 7 cm and height is 60 cm.
Answer:
Given,
Diameter of cylinder = 7 cm
Height of cylinder = 60 cm
So,
Radius of cylinder = 
Curved surface area of cylinder = 2πrh = 
Total surface area of cylinder = 
Question 2.
The curved surface area of a cylindrical road is 132 cm2. Find its length if the radius is 0.35 cm.
Answer:
Given,
Curved surface area of cylindrical road =132 cm2
Radius of road = 0.35 cm
Let length of road = h cm
So,
= 
=
= 
Length of road = 60 cm
Question 3.
The area of the base of a right circular cylinder is 616 cm2 and its height is 2.5 cm. Find the curved surface area of the cylinder.
Answer:
Given,
Area of base of right circular cylinder = 616 cm2
Height of cylinder = 2.5 cm
Let the radius of cylinder = r cm
So,
=
= 
=
∴ Curved surface area of cylinder = 
Question 4.
The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find its curved surface area and total surface area.
Answer:
Given,
Circumference of base of cylinder = 88 cm
Height of cylinder = 15 cm
So,
= 
Given
= 
Radius of cylinder = 14 cm
∴ Curved surface area of cylinder = 
∴ Total surface area area of cylinder = 
Question 5.
A rectangular strip 25 cm× 7 cm is rotated about the longer side. Find the total surface area of the solid thus generated.
Answer:
Given,
Dimension of rectangular strip = 25 cm × 7cm
When this strip is rotated about its longer side :
So,
Height of cylinder thus form = 25 cm
Radius = 7 cm
∴ Total surface area of cylinder =
Question 6.
A rectangular sheet of paper, 44 cm× 20 cm, is rolled along its length to form a cylinder. Find the total surface area of the cylinder thus generated.
Answer:
Given,
Dimensions of rectangular sheet of paper = 44cm × 20 cm
When this sheet of paper is rolled along its length:
So,
Circumference of base thus form = 44 cm
= 
= 
Radius = 7 cm
Height = 20 cm
∴ Total surface area of cylinder =
Question 7.
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their curved surface areas.
Answer:
Given,
Ratio of radius of two cylinder = 2:3
Ratio of their heights = 5:3
= 
So,
= 
Hence,
Ratio of their curved surface area would be = 10 : 9
Question 8.
The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Prove that its height and radius are equal.
Answer:
Given,
= 
Let radius of cylinder = r
Let height of cylinder = h
So,
= 
= 
= 
= 
=
, 
Question 9.
The curved surface area of a cylinder is 1320 cm2 and its base has diameter 21 cm. Find the height of the cylinder.
Answer:
Given,
Curved surface area of cylinder = 1320 cm2
Diameter of base = 21 cm
Radius of cylinder = 
Let height of cylinder = h cm
So,
= 
= 
Height of cylinder = 20 cm
Question 10.
The height of a right circular cylinder is 10.5 cm. If three times the sum of the areas of its two circular faces is twice the area of the curved surface area. Find the radius of its base.
Answer:
Given,
Height of cylinder = 10.5 cm
Let radius of cylinder = r cm
So,
Area of two bases of cylinder = 2πr2
Area of curved surface of cylinder = 2πrh
Now,
=
=
= 
= 
Radius of base of cylinder = 7 cm
Question 11.
Find the cost of plastering the inner surface of a well at Rs. 9.50 per m2, if it is 21 m deep and diamwter of its top is 6 m.
Answer:
Given,
Height of cylinder = 21 m
Diameter of cylinder = 6 m
Radius of cylinder = 
So,
Curved surface area of cylinder = 
∴ Cost of plastering the inner surface at rate Rs.9.50 per m2 = 396×9.50 = Rs.3762
Question 12.
A cylindrical vessel open at the top has diameter 20 cm and height 14 cm. Find the cost of tin-plating it on the inside at the rate of 50 paise per hundred square centimetre.
Answer:
Given,
Diameter of base of cylinder = 20 cm
Radius of cylinder = 
Height of cylinder = 14 cm
Total surface area of cylinder = 
∴ Cost of tin painting it inside at rate 50 paise per cm2 = 
Question 13.
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find the cost of plastering its inner curved surface at Rs. 4 per square metre.
Answer:
Given,
Inner diameter of circular well = 3.5 m
Radius of well = 
Height of well = 10 m
So,
Curved surface area of well = 
∴ Cost of plastering its inner curved surface at rate Rs. 4 per m2 = 110 ×4 = Rs. 440
Question 14.
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions moving monce over to level a playground. What is the area of the playground?
Answer:
Given,
Diameter of roller = 84 cm
Radius of roller = 
Length of roller = 120 cm
So,
Curved surface area of roller = 
No. of revolution it takes to leve
Hence,
Area of play ground = 500 × 31680 = 15840000 cm2 = 1584 m2
Question 15.
Twenty one cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m, what will be the cost of cleaning them at the rate of Rs. 2.50 per square matre?
Answer:
Given,
Number of pillars = 20
Diameter of pillar = 0.50 m
Radius of pillar = 
Height of pillar = 4 m
So,
Curved surface area of pillar = 
Curved surface area of 20 pillars = 20 × 
∴ Cost of cleaning them at rate Rs.2.50 per m2 = Rs. 
Question 16.
The total surface area of a hollow cylinder which is open from both sides if 4620 sq. cm, area of base ring is 115.5 sq. cm. and height 7 cm. Find the thickness of the cylinder.
Answer:
Given,
Total surface area of hollow cylinder = 4620 cm2
Area of base ring = 115.5 cm2
Height of cylinder = 7 cm
Let outer radius = R cm , inner radius = r cm
So,
Area of hollow cylinder = 
=2
Area of base = 
∴ 
= 
= 
= 
=
Thickness of cylinder = 
Question 17.
The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m2, find the circumference of its base.
Answer:
Given,
Sum of base radius and height of cylinder = 37 m
Total surface area = 1628 m2
So,
= r + h = 37
= 
= 
= 
Question 18.
Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.
Answer:
Given,
Radius of cylinder = 3.5 cm
Height of cylinder = 7.5 cm
So,
= 
Question 19.
A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs. 3.50 per 1000 cm2.
Answer:
Given,
Radius of base = 70 cm
Height of base = 1.4 m = 140 cm
So,
Area = 
Tin coating must be done on both side so Area = 
∴ Cost of tin coating at rate Rs.3.50 per 1000 cm2 = 
Exercise 22.2
Question 1.Find the volume of a cylinder whose
(i) r = 3.5 cm, h = 40 cm
(ii) r = 2.8 m, h = 15 m
Answer:
(i) Given,
r = 3.5 cm
h = 40 cm
Volume = 
(ii) Given,
r = 2.8 m
h =15 m
volume of cylinder = 
Question 2.
Find the volume of a cylinder, if the diameter (d) of its base and its altitude (h) are :
(i) d = 21 cm, h = 10 cm
(ii) d = 7 m, h = 24 m
Answer:
(i) Given,
D =21cm
r = 
h = 10 cm
Volume of cylinder = 
(ii) Given,
d = 7 m
r = 
h = 24 m
Volume of cylinder = 
Question 3.
The area of the base of a right circular cylinder is 616 cm2 and its height is 25 cm. Find the volume of the cylinder.
Answer:
Given,
Area of base = 616 cm2
Height = 25 cm
∴ volume of cylinder = 
Question 4.
The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find the volume of the cylinder.
Answer:
Given,
Circumference of base = 88 cm
Height = 15 cm
So,
=
= 
Volume of cylinder = 
Question 5.
A hollow cylindrical pipe is 21 dm long. Its outré and inner diameters are 10 cm and 6 cm respectively. Find the volume of the copper used in making the pipe.
Answer:
Given,
Length of cylinder = 21 dm = 210 cm
Outer diameter = 10 cm
Outer radius = 
Inner diameter = 6 cm
Inner radius = 
∴ Area of base = 
Volume of cylinder = 
Question 6.
Find the (i) curved surface area (ii) total surface area and (iii) volume of a right circular cylinder whose height is 15 cm and the radius of the base is 7 cm.
Answer:
Given,
Height of cylinder = 15 cm
Radius of base = 7 cm
i) Curved surface area = 
ii) Total surface area = 
iii) Volume of cylinder = 
Question 7.
The diameter of the base of a right circular cylinder is 42 cm and its height is 10 cm. Find the volume of the cylinder.
Answer:
Given,
Diameter of base of cylinder = 42 cm
Radius of base = 
Height = 10 cm
∴ volume of cylinder = 
Question 8.
Find the volume of cylinder, the diameter of whose base is 7 cm and height being 60 cm. Also, find the capacity of the cylinder in litres.
Answer:
Given,
Diameter of base = 7 cm
Radius of base =
Height of cylinder = 60 cm
∴ Volume of cylinder = 
Capacity of cylinder in litres = 
Question 9.
A rectangular strip 25 cm× 7 cm is rotated about the longer side. Find the volume of the solid, thus generated.
Answer:
Given,
Dimensions of rectangular srip = 25 cm × 7 cm
When it rotated about longer side :
Radius of base = 7 cm
Height of cylinder = 25 cm
∴ Volume of cylinder = 
Question 10.
A rectangular sheet of paper, 44 cm× 20 cm, is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.
Answer:
Given,
Dimensions of rectangular sheet = 44 cm×20 cm
When it rolled along its length :
Radius of base = 
Height of cylinder = 20 cm
∴ Volume of cylinder = 
Question 11.
The volume and the curved surface area of cylinder are 1650 cm3 and 660 cm2 respectively. Find the radius and height of the cylinder.
Answer:
Given,
Volume of cylinder = 1650 cm3
Curved surface area = 660 cm2
So,
= 
= 
= 
We have ,
Surface area = 660 cm2
= 
= 
Radius = 5 cm , height = 21 cm
Question 12.
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes.
Answer:
Given,
Ratio of radii of two cylinder = 2 : 3
= 
Ratio of their heights = 5 : 3
= 
∴ 
Ratio of volumes of two cylinder = 20 : 27
Question 13.
The ratio between the curved surface area dna the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area os 616 cm2.
Answer:
Given,
Total surface area of cylinder = 616 cm2
Ratio between curved surface area and total surface area of cylinder = 1 : 2
=
=
=
= 
= 
= 
= 
= 
Radius = 7 cm = height
∴ Volume of cylinder = 
Question 14.
The curved surface area of a cylinder is 1320 cm2 and its base has diameter 21 cm. Find the volume of the cylinder.
Answer:
Given,
Curved surface area = 1320 cm2
Diameter of base = 21 cm
Radius of base = 
So,
=
= 
= 
∴ Volume of cylinder = 
Question 15.
The ratio between the radius of the base and the height jof a cylinder is 2 : 3. Find the total surface area of the cylinder, if its volume is 1617 cm3.
Answer:
Given,
Ratio between radius and height of a cylinder = 2:3
= 
= 
Volume of cylinder = 1617 cm3
= 
= 
= 
= 
Radius = 7 cm
Height = 
∴ total surface area of cylinder = 
Question 16.
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and the height of the pillar.
Answer:
Given,
Curved surface area of cylinder = 264 m2
Volume = 924 m3
So,
= 
= 
Radius = 7 m
Diameter of cylinder = 2 × radius = 2×7 = 14 m
Curved surface area = 264 m2
= 
= 
= 
Height of cylinder = 6 m
Question 17.
Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radii.
Answer:
Given,
Volume of cylinder 1 = volume of cylinder 2
Ratio of their height = 1 : 2
= 
We have,
= 
= 
= 
= 
Question 18.
The height of a right circular cylinder is 10/5 m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder.
Answer:
Given,
Height of cylinder = 10.5 m
= 3( A+A) = 2 curved surface area (A= circular area of box)
= 
= 
= 
Volume of cylinder = 
Question 19.
How many cubic metres of earth must be dug-out to sink a well 21 m deep and 6 mdiameter?
Answer:
Given,
Height of cylinder = 21 m
Diameter of well = 6 m
radius of well =
so,
Amount of earth can be dug out from this well = 
Question 20.
The trunk of a tree is cylindrical and its circumference is 176 cm. If the length of the trunk is 3 m, find the volume of the timber that can be obtained from the trunk.
Answer:
Given,
Circumference of trunk of tree = 176 cm
Length of the trunk = 3m = 300 cm
so,
= 
= 
= 
hence,
Volume of timber can be obtained from trunk of tree = 
Question 21.
A well is dug 20 m deep and it has a diameter of 7 m. The earth which is so dug out is spread out on a rectangular plot 22 m long and 14 m broad. What is the height of the platform so formed?
Answer:
Given,
Depth of well = 20m
Diameter of well = 7 m
Radius of well =
Dimension of rectangular field = 22m × 14m
so,
Amount of earth dug out from well = 
when this earth is spread on rectangular field:
Then height of platform formed on rectangular field = 
Question 22.
A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.
Answer:
Given,
Diameter of well = 14 m
Radius of well = 
depth of well = 8 m
so,
Amount of earth dug out from well =
This earth is spread out on width of 21 m.
= Area ×h = 1232
= 
= 
=
Height of embankment = 53.3 cm
Question 23.
A cylindrical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimemsions 32 cm×22 cm×14 cm. Find the rise in the level of the water when the solid is completely submerged.
Answer:
Given,
Diameter of base of cylindrical vessel = 56 cm
Radius of base = 
Dimensions of rectangular solid vessel = 32 cm ×22 cm×14 cm
let rise in water level in vessel = h cm
so,
Volume of vessel = 
= 
= 
4 cm
Question 24.
A rectangular sheet of paper 30 cm× 18 cm can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.
Answer:
Given,
Dimensions of rectangular sheet = 30 cm× 18 cm
Case (i)
when paper is rolled along its length :
= 2πr = 30
= 
= height = 18 cm
Volume of cylinder thus formed = 
Case (ii)
When paper is rolled along its breadth :
= 2πr = 18
= 
= Height = 30 cm
Volume of cylinder thus formed = 
Hence,
= 
Question 25.
The rain which falls on a roof 18 m long and 16.5 m wide is allowed to be stored in a cylindrical tank 8 m in diameter. If it rains 10 cm on a day, what is the rise of water level in the tank due to it?
Answer:
Given,
Dimensions of roof = 18 m × 16.5 m
Diameter of cylindrical tank = 8 m
Radius of tank = 
it rains 10 cm a day
Let 'h' be the rise in level of tank
so,
= 
= 
= 
Question 26.
A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 5 cm. It is drawnout into a wire of diameter 1 mm. What will be the length of the wire so formed?
Answer:
Given,
Diameter of metallic cylinder = 1 cm
Radius of cylinder = 
Length of cylinder = 5 cm
Diameter of wire drawn from it = 1 mm = 0.1 cm
Let length of wire = h cm
so,
Length of wire drawn from metal = 
Question 27.
Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of copper weighs 8.4 gm.
Answer:
Given,
weight of copper wire = 13.2 kg
Diameter of wire = 4 mm
Radius of wire = 
Let length of wire = h cm
so,
weight of 1 cubic cm wire = 8.4 gm
= 
= 
Question 28.
2.2 cubic dm of brass is to be drawn into cylindrical wire 0.25 cm in diameter. Find the length of the wire.
Answer:
Given,
Volume of brass wire = 2.2 dm3 = 2200 cm3
Diameter of cylindrical wire = 0.25 cm
Radius of wire = 
Let length of wire = h cm
so,
= 
= 
Question 29.
The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq. cm. If the volume of the tube is 176 cuboc cm, find the inner and outer radii of the tube.
Answer:
Given,
length of cylindrical tube = 14 cm
Difference between inside and outside surface = 88 cm2
volume of cylinder = 176 cm3
let outer radius of tube = R cm
Let inner radius of tube = r cm
so,
= 
= 
dividing equation (i) by equation (ii)
= 
= 
= R+r = 4 ..................(iii)
from equation (ii)
= 
= 
= 
from equation (iii) and (iv)
= 2R = 5
= R = 
= r = 1.5 cm
Question 30.
Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?
Answer:
Given,
internal diameter of pipe = 2 cm
internal radius of pipe = 
rate of flow of water = 6 m/s = 600 cm/s
radius of base of cylindrical tank = 60 cm
so,
rise in height in cylindrical tank = 
Question 31.
A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.
Answer:
Given,
Internal diameter of cylindrical tube = 10.4 cm
internal radius of tube = 
length of tube = 25 cm
thickness of metal = 8 mm = 0.8 cm
so,
Outer radius of tube = R = 5.2+0.8 = 6 cm
Volume of metal = 
Question 32.
From a tap of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the pipe in one hour.
Answer:
Given,
inner radius of tap = 0.75 cm
Rate of water flow through it = 7 m/s = 700 cm/s
so,
volume of water per second derived from tap = 
Volume of water derived in 1 hour (3600 sec) = 
= 4455 litre
Question 33.
A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled?
Answer:
Given,
Diameter of cylindrical tank = 1.4 m
Radius of tank = 
Height of tank =2.1 m
Diameter of pipe flowing water in tank = 3.5 cm
Radius of pipe = 
cm
Rate of flow of water = 2 m/s
so,
Time taken to fill the tank = 
Question 34.
A rectangular sheet of paper 30 cm × 18 cm be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.
Answer:
Given,
Dimensions of rectangular sheet = 30 cm ×.18 cm
Case (i)
When sheet is rolled along its length:
= 
= 
height of cylinder = 18 cm
Hence , Volume of cylinder thus formed = 
Case (ii)
When sheet is rolled along its breadth :
= 
= 
Height of cylinder = 30 cm
Volume of cylinder = 
Hence,
Question 35.
How many litres of water flows out of a pipe having an area of cross section of 5 cm2 in one minute, if the speed of water in the pipe is 30 cm/sec?
Answer:
Given,
Cross section area of pipe = 5 cm2
Speed of water = 30 cm/s
Time = 1 minute = 60 sec
so,
Volume of water flows through pipe = 
= 
Question 36.
A solid cylinder has a total surface area of 231 cm2. It curved surface area is 
of the total surface area. Find the volume of the cylinder.
Answer:
Given,
Total surface area of cylinder = 231 cm2
Curved surface area = 
so,
= 
= 3 h = 2h + 2r
= h= 2r.............(i)
And,
= 
= 
= 
= 
= h = 2r = 2×3.5 = 7 cm
Volume of cylinder = 
Question 37.
Find the cost of sinking a tube well 280 m deep, having diameter 3 m at the rate of Rs. 3.60 per cubic metre. Find also the cost of cementing its inner curved surface at Rs. 2.50 per square metre.
Answer:
Given,
Depth of tube well = 280 m
Diameter of tube well = 3 m
Radius of well = 
so,
Volume = 
Cost of sinking tubewell at rate Rs.3.60/m3 = 1980×3.60 = Rs.7128
Curved surface area = 
Cost of cementing its inner curved surface at rate Rs.2.50/m2 = 2.50×2640 =Rs.6600
Question 38.
Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of copper weighs 8.4 gm.
Answer:
Given,
weight of copper wire = 13.2 kg
Diameter of wire = 4 mm
Radius of wire =
Let length of wire = h cm
so,
weight of 1 cubic cm wire = 8.4 gm
=
=
Question 39.
2.2 cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in diameter. Find the length of the wire.
Answer:
Given,
Volume of brass wire = 2.2 dm3 = 2200 cm3
Diameter of cylindrical wire = 0.25 cm
Radius of wire =
Let length of wire = h cm
so,
=
=
Question 40.
A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.
Answer:
Given,
Inside diameter of well = 10 m
Inside radius = 
depth of well = 8.4 m
Volume of earth dug out = 
Area of embankment formed = 
Height of embankment thus formed = 
Question 41.
A hollow garden roller, 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.
Answer:
Given,
Width of roller = 63 cm
Girth (perimeter) = 440 cm
= 2πR = 440
= 
= R= 
thickness of roller = 4 cm
inner radius = R - thickness = 70 - 4 = 66 cm
Volume of cylindrical iron = 
Question 42.
What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?
Answer:
Given,
Length of solid cylinder = L
diameter o cylinder = 2 cm
radius of cylinder =
Volume of cylinder = πr2L..............(i)
Length of hollow cylinder = 16 cm
External diameter = 20 cm
External radius =
thickness = 2.5 mm = 0.25 cm
so,
inner radius = 10 - 0.25 = 9.75 cm
Volume = 
From (i) and (ii)
= 
= L =79 cm
Question 43.
In the middle of a rectangular field measuring 30m ×20m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.
Answer:
Given,
Diameter of well = 7 m
Radius of well = 
Depth of well = 10 m
Volume of well = 
volume of well =Area of spread out × height of embankment
=
= 
= 
Height of embankment = 68.6 cm