# Surface Area And Volume

##### Class 8th Mathematics (new) MHB Solution

##### Class 8^{th} Mathematics (new) MHB Solution

**Practice Set 16.1**- Find the volume of a box if its length, breadth, and height are 20 cm, 10.5 cm and 8 cm…
- A cuboid shape soap bar has volume 150 cc. Find its thickness if its length is 10 cm…
- How many bricks of length 25 cm, breadth 15 cm, and height 10 cm are required to build…
- For rainwater harvesting, a tank of length 10 m, breadth 6 m, and depth 3m are built.…

**Practice Set 16.2**- In each example given below, the radius of the base of a cylinder and its height are…
- Find the total surface area of a closed cylindrical drum if its diameter is 50 cm and…
- Find the area of base and radius of a cylinder if its curved surface area is 660 sqcm…
- Find the area of the sheet required to make a cylindrical container which is open at…

**Practice Set 16.3**- Find the volume of the cylinder if height (h) and radius of the base (r) are as given…
- How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?…
- How much water will a tank hold if the interior diameter of the tank is 1.6 m and its…
- Find the volume of the cylinder if the circumference of the cylinder is 132 cm and…

**Practice Set 16.1**

- Find the volume of a box if its length, breadth, and height are 20 cm, 10.5 cm and 8 cm…
- A cuboid shape soap bar has volume 150 cc. Find its thickness if its length is 10 cm…
- How many bricks of length 25 cm, breadth 15 cm, and height 10 cm are required to build…
- For rainwater harvesting, a tank of length 10 m, breadth 6 m, and depth 3m are built.…

**Practice Set 16.2**

- In each example given below, the radius of the base of a cylinder and its height are…
- Find the total surface area of a closed cylindrical drum if its diameter is 50 cm and…
- Find the area of base and radius of a cylinder if its curved surface area is 660 sqcm…
- Find the area of the sheet required to make a cylindrical container which is open at…

**Practice Set 16.3**

- Find the volume of the cylinder if height (h) and radius of the base (r) are as given…
- How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?…
- How much water will a tank hold if the interior diameter of the tank is 1.6 m and its…
- Find the volume of the cylinder if the circumference of the cylinder is 132 cm and…

###### Practice Set 16.1

**Question 1.**Find the volume of a box if its length, breadth, and height are 20 cm, 10.5 cm and 8 cm respectively.

**Answer:**Given:

Length = 20 cm

Breadth = 10.5 cm

Height = 8 cm

The box is nothing but a cuboid

**Volume****of cuboid = l × b × h**

= 20 × 10.5 × 8

= 1680 cm^{3}

∴The volume of the box is 1680 cm^{3}

**Question 2.**A cuboid shape soap bar has volume 150 cc. Find its thickness if its length is 10 cm and breadth is 5 cm.

**Answer:**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

**Question 3.**How many bricks of length 25 cm, breadth 15 cm, and height 10 cm are required to build a wall of length 6 m, height 2.5 m, and breadth 0.5 m?

**Answer:**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 cm^{3}

The volume of one brick = l × b × h

= 25 × 15 × 10

= 3750 cm^{3}

= 2000 bricks

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

**Question 4.**For rainwater harvesting, a tank of length 10 m, breadth 6 m, and depth 3m are built. What is the capacity of the tank? How many liters of water can it hold?

**Answer:**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 m^{3}

The capacity of the tank is 180 m^{3}

Now,

1 m^{3} = 1000 litre

∴180 m^{3} = 180 × 1000 = 180,000 litre

∴ The tank can hold 180,000 litres of water

**Question 1.**

Find the volume of a box if its length, breadth, and height are 20 cm, 10.5 cm and 8 cm respectively.

**Answer:**

Given:

Length = 20 cm

Breadth = 10.5 cm

Height = 8 cm

The box is nothing but a cuboid

**Volume****of cuboid = l × b × h**

= 20 × 10.5 × 8

= 1680 cm^{3}

∴The volume of the box is 1680 cm^{3}

**Question 2.**

A cuboid shape soap bar has volume 150 cc. Find its thickness if its length is 10 cm and breadth is 5 cm.

**Answer:**

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

**Question 3.**

How many bricks of length 25 cm, breadth 15 cm, and height 10 cm are required to build a wall of length 6 m, height 2.5 m, and breadth 0.5 m?

**Answer:**

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 cm^{3}

The volume of one brick = l × b × h

= 25 × 15 × 10

= 3750 cm^{3}

= 2000 bricks

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

**Question 4.**

For rainwater harvesting, a tank of length 10 m, breadth 6 m, and depth 3m are built. What is the capacity of the tank? How many liters of water can it hold?

**Answer:**

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 m^{3}

The capacity of the tank is 180 m^{3}

Now,

1 m^{3} = 1000 litre

∴180 m^{3} = 180 × 1000 = 180,000 litre

∴ The tank can hold 180,000 litres of water

###### Practice Set 16.2

**Question 1.**In each example given below, the radius of the base of a cylinder and its height are given. Then find the curved surface area and total surface area.

(1) r = 7 cm, h = 10 cm

(2) r = 1.4 cm, h = 2.1 cm

(3) r = 2.5 cm, h = 7 cm

(4) r = 70 cm, h = 1.4 cm

(5) r = 4.2 cm, h = 14 cm

**Answer:****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 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 7(10+7)

**=** 748 cm^{2}

2. r = 1.4 cm, h = 2.1 cm

CSA = 2πrh

**=** 2 × 3.14 × 1.4 × 2.1

**=** 18.48 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 1.4(2.1+1.4)

**=** 30.8 cm^{2}

3. r = 2.5 cm, h = 7 cm

CSA = 2πrh

**=** 2 × 3.14 × 2.5 × 7

**=** 110 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 2.5(7+2.5)

**=** 149.29 cm^{2}

4. r = 70 cm, h = 1.4 cm

CSA = 2πrh

**=** 2 × 3.14 × 70 × 1.4

**=** 616 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 70(70+1.4)

**=** 31416 cm^{2}

5. r = 4.2 cm, h = 14 cm

CSA = 2πrh

**=** 2 × 3.14 × 4.2 × 14

**=** 369.6 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 4.2(4.2+14)

**=** 480.48 cm^{2}

**Question 2.**Find the total surface area of a closed cylindrical drum if its diameter is 50 cm and height is 45 cm. (π = 3.14)

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

Here,

h = 45 cm

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

**=** 10990 cm^{2}

Total Surface Area of Cylinder is 10990 cm^{2}

**Question 3.**Find the area of base and radius of a cylinder if its curved surface area is 660 sqcm and height is 21 cm

**Answer:**Area of base of cylinder = π × r^{2}

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 × r^{2}

= 3.14 × 25 × 25

**=** 78.5 cm^{2}

Area of the base is 78.5 cm^{2} and radius is 5 cm

**Question 4.**Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is 28 cm and height is 20 cm. Find the approximate area of the sheet required to make a lid of height 2 cm for this container.

**Answer:**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 × r^{2}

Curved surface area = 2π × r × h

**∴****Area of Cylinder =****π × r**^{2} + 2π × r × h

= 3.14 × 14^{2} + 2 × 3.14 × 14 × 20

= 615.44 + 1759.3

= 2376 cm^{2}

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

∴ Area of Sheet = 2376 cm^{2}

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 × r^{2} + 2π × r × h

= 3.14 × 14^{2} + 2 × 3.14 × 14 × 2

= 615.44 + 175.84

= 792 cm^{2}

∴ Area of Sheet = 2376 cm^{2}

∴ Area of Lid = 792 cm^{2}

**Question 1.**

In each example given below, the radius of the base of a cylinder and its height are given. Then find the curved surface area and total surface area.

(1) r = 7 cm, h = 10 cm

(2) r = 1.4 cm, h = 2.1 cm

(3) r = 2.5 cm, h = 7 cm

(4) r = 70 cm, h = 1.4 cm

(5) r = 4.2 cm, h = 14 cm

**Answer:**

**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 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 7(10+7)

**=** 748 cm^{2}

2. r = 1.4 cm, h = 2.1 cm

CSA = 2πrh

**=** 2 × 3.14 × 1.4 × 2.1

**=** 18.48 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 1.4(2.1+1.4)

**=** 30.8 cm^{2}

3. r = 2.5 cm, h = 7 cm

CSA = 2πrh

**=** 2 × 3.14 × 2.5 × 7

**=** 110 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 2.5(7+2.5)

**=** 149.29 cm^{2}

4. r = 70 cm, h = 1.4 cm

CSA = 2πrh

**=** 2 × 3.14 × 70 × 1.4

**=** 616 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 70(70+1.4)

**=** 31416 cm^{2}

5. r = 4.2 cm, h = 14 cm

CSA = 2πrh

**=** 2 × 3.14 × 4.2 × 14

**=** 369.6 cm^{2}

TSA = 2πr(h+r)

**=** 2 × 3.14 × 4.2(4.2+14)

**=** 480.48 cm^{2}

**Question 2.**

Find the total surface area of a closed cylindrical drum if its diameter is 50 cm and height is 45 cm. (π = 3.14)

**Answer:**

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

Here,

h = 45 cm

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

**=** 10990 cm^{2}

Total Surface Area of Cylinder is 10990 cm^{2}

**Question 3.**

Find the area of base and radius of a cylinder if its curved surface area is 660 sqcm and height is 21 cm

**Answer:**

Area of base of cylinder = π × r^{2}

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 × r^{2}

= 3.14 × 25 × 25

**=** 78.5 cm^{2}

Area of the base is 78.5 cm^{2} and radius is 5 cm

**Question 4.**

Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is 28 cm and height is 20 cm. Find the approximate area of the sheet required to make a lid of height 2 cm for this container.

**Answer:**

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 × r^{2}

Curved surface area = 2π × r × h

**∴****Area of Cylinder =****π × r ^{2} + 2π × r × h**

= 3.14 × 14^{2} + 2 × 3.14 × 14 × 20

= 615.44 + 1759.3

= 2376 cm^{2}

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

∴ Area of Sheet = 2376 cm^{2}

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 × r^{2} + 2π × r × h

= 3.14 × 14^{2} + 2 × 3.14 × 14 × 2

= 615.44 + 175.84

= 792 cm^{2}

∴ Area of Sheet = 2376 cm^{2}

∴ Area of Lid = 792 cm^{2}

###### Practice Set 16.3

**Question 1.**Find the volume of the cylinder if height (h) and radius of the base (r) are as given below.

(1) r = 10.5 cm, h = 8 cm

(2) r = 2.5 m, h = 7 m

(3) r = 4.2 cm, h = 5 cm

(4) r = 5.6 cm, h = 5 cm

**Answer:****Volume of cylinder****=****π × r**^{2} × h

1. r = 10.5 cm, h = 8 cm

Volume = π × r^{2} × h

= 3.14 × 10.5^{2} × 8

= 2772 cm^{3}

2. r = 2.5 m, h = 7 m

Volume = π × r^{2} × h

= 3.14 × 2.5^{2} × 7

= 137.5 cm^{3}

3. r = 4.2 cm, h = 5 cm

Volume = π × r^{2} × h

= 3.14 × 4.2^{2} × 5

= 277.2 cm^{3}

4. r = 5.6 cm, h = 5 cm

Volume = π × r^{2} × h

= 3.14 × 5.6^{2} × 5

= 492.8 cm^{3}

**Question 2.**How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?

**Answer:**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 × r^{2} × h

= 3.14 × 0.7^{2} × 90

= 138.6 cm^{3}

∴ Amount of iron required is 138.6 cm^{3}

**Question 3.**How much water will a tank hold if the interior diameter of the tank is 1.6 m and its depth is 0.7 m?

**Answer:**Given,

Radius

Height = 0.7 m

The volume of tank = π × r^{2} × h

= 3.14 × 0.8^{2} × 0.7

= 1.408 m^{3}

Now, 1m^{3} = 1000 litre

1.408 m^{3} = 1408 litre

∴ The tank can hold 1408 liter of water

**Question 4.**Find the volume of the cylinder if the circumference of the cylinder is 132 cm and height is 25 cm.

**Answer:**Given,

Circumference = 132 cm

Height = 25 cm

Volume = ?

The circumference of cylinder = 2 × π × r

132 = 2 × π × r

The volume of cylinder = π × r^{2} × h

= 3.14 × 21^{2} × 25

= 34650 cm^{3}

∴ The volume of the cylinder is 34650 cm^{3}

**Question 1.**

Find the volume of the cylinder if height (h) and radius of the base (r) are as given below.

(1) r = 10.5 cm, h = 8 cm

(2) r = 2.5 m, h = 7 m

(3) r = 4.2 cm, h = 5 cm

(4) r = 5.6 cm, h = 5 cm

**Answer:**

**Volume of cylinder****=****π × r ^{2} × h**

1. r = 10.5 cm, h = 8 cm

Volume = π × r^{2} × h

= 3.14 × 10.5^{2} × 8

= 2772 cm^{3}

2. r = 2.5 m, h = 7 m

Volume = π × r^{2} × h

= 3.14 × 2.5^{2} × 7

= 137.5 cm^{3}

3. r = 4.2 cm, h = 5 cm

Volume = π × r^{2} × h

= 3.14 × 4.2^{2} × 5

= 277.2 cm^{3}

4. r = 5.6 cm, h = 5 cm

Volume = π × r^{2} × h

= 3.14 × 5.6^{2} × 5

= 492.8 cm^{3}

**Question 2.**

How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?

**Answer:**

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 × r^{2} × h

= 3.14 × 0.7^{2} × 90

= 138.6 cm^{3}

∴ Amount of iron required is 138.6 cm^{3}

**Question 3.**

How much water will a tank hold if the interior diameter of the tank is 1.6 m and its depth is 0.7 m?

**Answer:**

Given,

Radius

Height = 0.7 m

The volume of tank = π × r^{2} × h

= 3.14 × 0.8^{2} × 0.7

= 1.408 m^{3}

Now, 1m^{3} = 1000 litre

1.408 m^{3} = 1408 litre

∴ The tank can hold 1408 liter of water

**Question 4.**

Find the volume of the cylinder if the circumference of the cylinder is 132 cm and height is 25 cm.

**Answer:**

Given,

Circumference = 132 cm

Height = 25 cm

Volume = ?

The circumference of cylinder = 2 × π × r

132 = 2 × π × r

The volume of cylinder = π × r^{2} × h

= 3.14 × 21^{2} × 25

= 34650 cm^{3}

∴ The volume of the cylinder is 34650 cm^{3}