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Surface Area And Volume (cube-cuboid)

Class 8th Mathematics AP Board Solution
Exercise 14.1
  1. There are two cuboidal boxes as shown in the given figure. Which box requires…
  2. Find the side of a cube whose surface area is 600 cm^2 .
  3. Prameela painted the outer surface of a cabinet of measures 1m × 2m × 1.5m.…
  4. Find the cost of painting a cuboid of dimensions 20cm × 15 cm × 12 cm at the…
Exercise 14.2
  1. Find the volume of the cuboid whose dimensions are given below.
  2. Find the capacity of the tanks with the following internal dimensions. Express…
  3. What will happen to the volume of a cube if the length of its edge is reduced…
  4. Find the volume of each of the cube whose sides are. (i) 6.4 cm (ii) 1.3 m…
  5. How many bricks will be required to build a wall of 8 m long, 6m height and…
  6. A cuboid is 25 cm long, 15 cm broad, and 8 cm high. How much of its volume will…
  7. A closed box is made up of wood which is 1cm thick. The outer dimensions of the…
  8. How many cubes of edge 4cm, each can be cut out from cuboid whose length,…
  9. How many cuboids of size 4 cm × 3 cm × 2 cm can be made from a cuboid of size…
  10. A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be…
Exercise 14.1
Question 1.

There are two cuboidal boxes as shown in the given figure. Which box requires the less amount of material to make?
Answer:

Measurement of box 1

Length = 60 cm,


Breadth = 40 cm and,


Height = 50 cm


Volume of cuboid = Length × Breadth × Height


= 60 × 40 × 20


= 12000 cm3


Measurement of box 2


Side = 50cm


Volume of cube = (side)3


= (50)3


= 50 × 50 × 50


= 125000 cm3


Box 1 requires less amount of material.
Question 2.

Find the side of a cube whose surface area is 600 cm2.
Answer:

Let the side be S.

∴ surface area of cube = 6× side2


⇒ 600 = 6 × s2


⇒ = s2


⇒ s2 = 100


⇒ s = √100


⇒ s = 10 cm
Question 3.

Prameela painted the outer surface of a cabinet of measures 1m × 2m × 1.5m. Find the surface area she cover if she painted all except the bottom of the cabinet?
Answer:

Measurement of the cuboid

Length(L) = 1 m breadth(B) = 2 m and height(H) = 1.5 m


Total surface area = 2(LB + BH + LH)


= 2(1 × 2 + 2 × 1.5 + 1 × 1.5)


= 2(2 + 3 + 1.5)


= 2(6.5)


= 13 cm2


Area of bottom surface = 1 × 2 = 2m2


Hence, area covered by painting = 13 – 2 = 11 m2
Question 4.

Find the cost of painting a cuboid of dimensions 20cm × 15 cm × 12 cm at the rate of 5 paisa per square centimeter.
Answer:

Measurement of the cuboid

Length(L) = 20 cm breadth(B) = 15 cm and height(H) = 12cm


Total surface area = 2(LB + BH + LH)


= 2(20 × 15 + 15 × 12 + 20 × 12)


= 2(300 + 180 + 240)


= 2(720)


= 1440 cm2


Rate of painting 1cm2 = ₹0.05


Rate of painting a whole cuboid = 0.05 × 1440


= ₹72
Exercise 14.2
Question 1.

Find the volume of the cuboid whose dimensions are given below.
Answer:

i: Length = 8.2 m Breadth = 5.3m and Height = 2.6m

Volume of cuboid = Length × Breadth × Height


= 8.2 × 5.3 × 2.6


= 112.996 m3


ii: Length = 5.0 m Breadth = 4.0m and Height = 3.5m


Volume of cuboid = Length × Breadth × Height


= 5 × 4 × 3.5


= 70 m3


iii: Length = 4.5 m Breadth = 2m and Height = 2.5m


Volume of cuboid = Length × Breadth × Height


= 4.5 × 2 × 2.5


= 22.5 m3
Question 2.

Find the capacity of the tanks with the following internal dimensions. Express the capacity in cubic meters and liters for each tank.
Answer:

i: Length = 3m 20cm = 3.2m

Breadth = 2m 90cm = 2.9m


Height = 1m 50cm = 1.5m


Volume of cuboid = Length × Breadth × Height


= 3.2 × 2.9 × 1.5


= 13.92 m3


ii: Length = 2m 50cm = 2.5m


Breadth = 1m 60cm = 1.6m


Height = 1m 30cm = 1.3m


Volume of cuboid = Length × Breadth × Height


= 2.5 × 1.6 × 1.3


= 5.2 m3


iii: Length = 7m 30cm = 7.3m


Breadth = 3m 60cm = 3.6m


Height = 1m 40cm = 1.4m


Volume of cuboid = Length × Breadth × Height


= 7.3 × 3.6 × 1.4


= 36.792 m3
Question 3.

What will happen to the volume of a cube if the length of its edge is reduced to half? Is the volume get reduced? If yes, how much?
Answer:

Let x be the length of the cube

Volume of cube = (side)3


= x3


If the length of its edge is reduced to half, then length would be =


Now, Volume of cube =


=


Yes, the volume gets reduced by m3.
Question 4.

Find the volume of each of the cube whose sides are.

(i) 6.4 cm (ii) 1.3 m (iii) 1.6 m.
Answer:

(i) Side = 6.4cm

Volume of cube = (side)3


= (6.4) 3


= 6.4 × 6.4 × 6.4


= 262.144 cm3


(ii) Side = 1.3cm


Volume of cube = (side)3


= (1.3) 3


= 1.3 × 1.3 × 1.3


= 2.197 m3


(iii) Side = 1.6m


Volume of cube = (side)3


= (1.6) 3


= 1.6 × 1.6 × 1.6


= 4.096 m3
Question 5.

How many bricks will be required to build a wall of 8 m long, 6m height and 22.5 cm thick, if each brick measures 25 cm by 11.25 cm by 6 cm?
Answer:

Measurements of Wall:

Length = 800cm Breadth = 600cm and Height = 22.5cm


Volume of wall = Length × Breadth × Height


= 800 × 600 × 22.5


Measurements of Brick:


Length = 25cm Breadth = 11.25cm and Height = 6cm


Volume of wall = Length × Breadth × Height


= 25 × 11.25 × 6


Number of bricks required build a wall =


=


= 32 × 100 × 2


= 64 × 100


= 6400


Hence, 6400 bricks are required to build the wall.
Question 6.

A cuboid is 25 cm long, 15 cm broad, and 8 cm high. How much of its volume will differ from that of a cube with the edge of 16 cm?
Answer:

Measurement of cuboid

Length = 25 cm Breadth = 15 cm and Height = 8 cm


Volume of cuboid = Length × Breadth × Height


= 25 × 15 × 8


= 3000 cm3


Measurement of cube


Side = 16cm


Volume of cube = (side)3


= (16) 3


= 16 × 16 × 16


= 4096 cm3


Difference between the volumes = 4096 – 3000 cm3 = 1096 cm3


Volume of cuboid differs from volume of cube by 1096 cm3.
Question 7.

A closed box is made up of wood which is 1cm thick. The outer dimensions of the box is 5 cm × 4 cm × 7 cm. Find the volume of the wood used.
Answer:

Measurement of box from outside:

Length = 5 cm Breadth = 4 cm and Height = 7 cm


Volume of cuboid = Length × Breadth × Height


= 5 cm × 4 cm × 7 cm


= 140 cm3


Measurement of box from the inside


Length = 4 cm

Breadth = 3 cm and

Height = 6 cm


Volume of cuboid = Length × Breadth × Height


= 4 cm × 3 cm × 6 cm


= 72 cm3


Volume of wood used = volume of the box from outside – volume of the box from inside


= 140 – 72


= 68 cm3
Question 8.

How many cubes of edge 4cm, each can be cut out from cuboid whose length, breadth and height are 20 cm, 18 cm and 16 cm respectively.
Answer:

Measurement of cuboid

Length = 20 cm Breadth = 18 cm and Height = 16 cm


Volume of cuboid = Length × Breadth × Height


= 20 × 18 × 16


= 5760 cm3


Measurement of cube


Side = 4 cm


Volume of cube = (side)3


= (4) 3


= 4 × 4 × 4


= 64 cm3


Number of cube which can be cut from the cuboid =


=


=


= 90


90 cubes can be cut out from the cuboid.
Question 9.

How many cuboids of size 4 cm × 3 cm × 2 cm can be made from a cuboid of size 12 cm × 9 cm × 6 cm?
Answer:

Measurement of bigger cuboid

Length = 12 cm Breadth = 9 cm and Height = 6 cm


Volume of cuboid = Length × Breadth × Height


= 12cm × 9cm × 6cm


Measurement of smaller cuboid


Length = 4 cm Breadth = 3 cm and Height = 2 cm


Volume of cuboid = Length × Breadth × Height


= 4cm × 3cm × 2cm


Number of smaller cuboids which can be made from bigger cuboid


=


=


= 3 × 3 × 3


= 27 cuboids


27 cuboids of smaller cuboids can be made from bigger cuboid.
Question 10.

A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be its height to hold 4.5 liters of water?
Answer:

We know that,

1 liter is 1000cm3,


∴ 4.5 liters = 4.5 × 1000 = 4500 cm3


Measurement of vessel


Length = 30 cm,


Breadth = 25cm,


And Height =?


Let the height be h cm.


We are given the capacity which this vessel can hold i.e. the volume of the vessel.


Volume of vessel = Length × Breadth × Height


4500 = 300 × 25 × h cm


4500 = 750 × h


h =


h =


h = 6 cm


Hence, height of the vessel is 6cm which can hold 4.5 liters.