Surface Area And Volume

Given:

Length = 20 cm

Breadth = 10.5 cm

Height = 8 cm

The box is nothing but a cuboid

Volumeof cuboid = l × b × h

= 20 × 10.5 × 8

= 1680 cm³

∴The volume of the box is 1680 cm³

Given:

Volume of soap bar = 150 cc

Length = 10 cm

Breadth = 5 cm

Height = ?

The volume of cuboid = l × b × h

150 = 10 × 5 × h

h = 3 cm

The height of soap bar is 3 cm

Given:

For one brick,

Length = 25 cm, breadth = 15 cm, height = 10 cm

For wall,

Length = 6 m = 6 × 100 cm = 600 cm

Breadth = 0.5 m = 0.5 × 100 = 50 cm

Height = 2.5 m 2.5 × 100 = 250 cm

Now, the number of bricks required to build a wall is given by,

Both wall and brick are cuboidal in shape.

Hence, the volume is given by,

The volume of wall = l × b × h

= 600 × 50 × 250

= 7500000 cm³

The volume of one brick = l × b × h

= 25 × 15 × 10

= 3750 cm³

= 2000 bricks

∴2000 bricks are required to build a wall of dimensions 6 × 0.5 × 2 m.

Given:

Length of tank = 10 m

Breadth of tank = 6 m

The height of tank = 3 m

Capacity is nothing but the volume of the tank.

As for length, breadth and height are given, the tank is cuboidal in shape.

The volume of tank = l × b × h

= 10 × 6 × 3

= 180 m³

The capacity of the tank is 180 m³

Now,

1 m³ = 1000 litre

∴180 m³ = 180 × 1000 = 180,000 litre

∴ The tank can hold 180,000 litres of water

Curved surface area of cylinder(CSA) = 2πrh

Total surface area of cylinder(TSA) = 2πr(h+r)

1. r = 7 cm, h = 10 cm

CSA = 2πrh

= 2 × 3.14 × 7 × 10

= 440 cm²

TSA = 2πr(h+r)

= 2 × 3.14 × 7(10+7)

= 748 cm²

2. r = 1.4 cm, h = 2.1 cm

CSA = 2πrh

= 2 × 3.14 × 1.4 × 2.1

= 18.48 cm²

TSA = 2πr(h+r)

= 2 × 3.14 × 1.4(2.1+1.4)

= 30.8 cm²

3. r = 2.5 cm, h = 7 cm

CSA = 2πrh

= 2 × 3.14 × 2.5 × 7

= 110 cm²

TSA = 2πr(h+r)

= 2 × 3.14 × 2.5(7+2.5)

= 149.29 cm²

4. r = 70 cm, h = 1.4 cm

CSA = 2πrh

= 2 × 3.14 × 70 × 1.4

= 616 cm²

TSA = 2πr(h+r)

= 2 × 3.14 × 70(70+1.4)

= 31416 cm²

5. r = 4.2 cm, h = 14 cm

CSA = 2πrh

= 2 × 3.14 × 4.2 × 14

= 369.6 cm²

TSA = 2πr(h+r)

= 2 × 3.14 × 4.2(4.2+14)

= 480.48 cm²

Total surface area of cylinder(TSA) = 2πr(h+r)

Here,

h = 45 cm

Total Surface Area = 2 × 3.14 × 25(45+25)

= 10990 cm²

Total Surface Area of Cylinder is 10990 cm²

Area of base of cylinder = π × r²

Curved surface area of cylinder(CSA) = 2π × r × h

Here, CSA = 660 sqcm, h = 21 cm, r = ?

CSA = 2π × r × h

660 = 2π × r × 21

r = 5 cm

Area of base = π × r²

= 3.14 × 25 × 25

= 78.5 cm²

Area of the base is 78.5 cm² and radius is 5 cm

Given:

Diameter = 28 cm

Radius height = 2 cm

As the cylindrical container is open at one side, Total area of a cylinder is given as,

Area of Cylinder = area of the base + curved surface area

Area of base = π × r²

Curved surface area = 2π × r × h

∴Area of Cylinder =π × r² + 2π × r × h

= 3.14 × 14² + 2 × 3.14 × 14 × 20

= 615.44 + 1759.3

= 2376 cm²

Now, the area of the sheet required to make a cylindrical container is nothing but an area of the cylinder.

∴ Area of Sheet = 2376 cm²

Now, we need to make a lid for the open cylinder. Given the height of the lid is 2 cm.

As the lid is for the cylinder, it’s radius will be the radius of the cylinder.

Hence, For lid,

Radius = 14 cm

Height = 2 cm

Area of lid = area of the base of the lead + curved surface area

= π × r² + 2π × r × h

= 3.14 × 14² + 2 × 3.14 × 14 × 2

= 615.44 + 175.84

= 792 cm²

∴ Area of Sheet = 2376 cm²

∴ Area of Lid = 792 cm²

Volume of cylinder=π × r² × h

1. r = 10.5 cm, h = 8 cm

Volume = π × r² × h

= 3.14 × 10.5² × 8

= 2772 cm³

2. r = 2.5 m, h = 7 m

Volume = π × r² × h

= 3.14 × 2.5² × 7

= 137.5 cm³

3. r = 4.2 cm, h = 5 cm

Volume = π × r² × h

= 3.14 × 4.2² × 5

= 277.2 cm³

4. r = 5.6 cm, h = 5 cm

Volume = π × r² × h

= 3.14 × 5.6² × 5

= 492.8 cm³

Given,

length/height of the cylindrical rod = 90 cm

The radius of rod

Here, we need to calculate the amount of iron required to make a rod.

That mean, we need to calculate the volume of the rod.

Volume of rod = π × r² × h

= 3.14 × 0.7² × 90

= 138.6 cm³

∴ Amount of iron required is 138.6 cm³

Given,

Radius

Height = 0.7 m

The volume of tank = π × r² × h

= 3.14 × 0.8² × 0.7

= 1.408 m³

Now, 1m³ = 1000 litre

1.408 m³ = 1408 litre

∴ The tank can hold 1408 liter of water

Given,

Circumference = 132 cm

Height = 25 cm

Volume = ?

The circumference of cylinder = 2 × π × r

132 = 2 × π × r

The volume of cylinder = π × r² × h

= 3.14 × 21² × 25

= 34650 cm³

∴ The volume of the cylinder is 34650 cm³