Volume of Cylinders-Geometry-Solved Examples

Solved Examples and Worksheet for Volume of Cylinders

Q1Johnny made a cylinder using cardboard paper. What is the volume of the cylinder, if its base radius is 7 in and height is 9 in?
(Volume = πr²h)

A. 441π in³
B. 450π in³
C. 432π in³
D. none of these

Solutions

Step: 1

The volume of a cylinder = πr²h

[Formula.]

Step: 2

= π × 7² × 9

[Substitute r = 7 and h = 9.]

Step: 3

= 441π in ³

[Simplify.]

Step: 4

So, the volume of the cylinder that Johnny made is 441π in ³.

Correct Answer is : 441π in³

Q2A water tank is 60 ft long and 40 ft wide. If the depth of water is 20 ft, then what is the volume of the water in the tank?

A. 48000 ft³
B. 4400 ft³
C. 49000 ft³
D. 47000 ft³

Solutions

Step: 1

Length of the water tank = 60 ft.

Step: 2

Width of the water tank = 40 ft.

Step: 3

The height of the water level = 20 ft.

Step: 4

Volume of water in the tank = length × width × depth.

Step: 5

= 60 × 40 × 20

[Substitute l = 60, w = 40 and h = 20.]

Step: 6

= 48000 ft³

[Multiply 60, 40 and 20.]

Step: 7

Volume of water in the tank is 48000 ft³.

Correct Answer is : 48000 ft³

Q3What is the volume of a cylinder with a base area of 7 in.² and height 5 in.?
A. 35 in.³
B. 12 in.³
C. 2 in.³
D. 7 in.³

Solutions

Step: 1

Volume of a cylinder = Base area × height of the cylinder

Step: 2

= 7 × 5

[Substitute the values.]

Step: 3

= 35 in.³

[Multiply.]

Step: 4

So, the volume of the cylinder is 35 in.³.

Correct Answer is : 35 in.³

Q4Find the volume of a cylinder whose radius is 3 units and height is 21 units. [Use π = 227]
A. 27 cubic units
B. 198 cubic units
C. 594 cubic units
D. 4158 cubic units

Solutions

Step: 1

The formula for the volume of a cylinder is πr²h, where r is the radius of its base and h is its height.

Step: 2

Volume of the cylinder = π × 3² × 21

[Substitute the values of the base radius and the height.]

Step: 3

= 227 × 9 × 21

[Substitute π = 227.]

Step: 4

= 41587

[Multiply the numbers in the numerator.]

Step: 5

= 594

[Divide.]

Step: 6

So, the volume of the cylinder is 594 cubic units.

Correct Answer is : 594 cubic units

Q5The capacity of a cylindrical tank is 7687 cm³. If the diameter of its base is 24 cm then find its height. (Round to the nearest cm.)

A. 17 cm
B. 51 cm
C. 27 cm
D. 34 cm

Solutions

Step: 1

Base diameter of cylindrical tank =24 cm

Step: 2

Radius = diameter2 = 242 = 12 cm.

Step: 3

Capacity of a cylindrical tank = πr²h

[Formula.]

Step: 4

πr²h = 7687

Step: 5

3.14 × 12² × h = 7687

[Substitute the values.]

Step: 6

452.16 h = 7687

[Multiply.]

Step: 7

h = 7687452.16

[Divide each side by 452.16]

Step: 8

h = 17.0006

[Simplify.]

Step: 9

h = 17

[Round to the nearest cm.]

Step: 10

Height of the cylindrical tank = 17 cm

Correct Answer is : 17 cm

Q6By how many times will the volume of a cylinder increase, if the height of the cylinder is increased by 8 times keeping the radius constant?
A. 512 times
B. 8 times
C. 24 times
D. 64 times

Solutions

Step: 1

Let r and h be the radius and height of the cylinder, respectively.

Step: 2

Volume of the cylinder = πr²h

[Formula.]

Step: 3

The height of the cylinder, after increasing it by 8 times is 8h.

Step: 4

Volume of the cylinder after increasing its height = π × r² × 8h

[Substitute h = 8h.]

Step: 5

= 8πr²h

[Simplify.]

Step: 6

= 8 × original volume of the cylinder

Step: 7

So, the volume of the cylinder becomes 8 times the original volume.

Correct Answer is : 8 times

Q7A circular tank of thickness 30 cm and height 80 cm whose diameter is 4 m is to be constructed in a storage yard. The rate of construction is $10 per m³. Find the cost of construction. [Take π = 3.]
A. $284
B. $14.94
C. $30.96
D. $3090

Solutions

Step: 1

Inner radius of the tank = d2= 2 m = 200 cm

[Radius = Diameter2.]

Step: 2

Outer radius of the tank = 200 + 30 = 230 cm

[Radius + thickness of the tank.]

Step: 3

Height of the tank = 80 cm

[Given.]

Step: 4

Volume of the tank = Volume of outer cylinder - Volume of the inner cylinder

[Formula.]

Step: 5

Volume of the outer cylinder = 3 × (230)² × 80 = 12696000 cm³

[Volume of the cylinder = π r² h.]

Step: 6

Volume of the inner cylinder = 3 × (200)² × 80 = 9600000 cm³

[Volume of the cylinder = π r² h.]

Step: 7

Volume of the tank = 12696000 - 9600000 = 3096000 cm³ = 3.096 m³

[Substitute in step 4.]

Step: 8

Rate of construction = $10 per m³

[Given.]

Step: 9

Cost of construction = 3.096 m³ × 10 = $30.96

[Simplify.]

Correct Answer is : $30.96

Q8A golden bar of length 1.20 m and cross section 16 cm × 15 cm is used to make circular chains of length 56 cm and diameter 5 mm. How many such chains can be made? [Take π = 3.]

A. 2929
B. 2743
C. 2786
D. 2777

Solutions

Step: 1

Number of chains that can be made = Volume of the golden bar Volume of one chain

[Formula.]

Step: 2

Volume of the golden bar = 1.20 × 100 ×16 × 15 = 28800 cm³

[Convert meter to centimeter.]

Step: 3

Radius of the chain = 52= 2.5 mm = 0.25 cm

[Radius = Diameter2.]

Step: 4

Volume of one chain = 3 × (0.25)² × 56 = 10.50 cm³

[Volume of a cylinder = π r² h.]

Step: 5

Number of chains = 2880010.50= 2743 chains (approximately)

[From steps 2 and 4.]

Correct Answer is : 2743

Q9By how many times will the volume of a cylinder increase, if the height of the cylinder is increased by 3 times, keeping the radius constant?

A. 3 times
B. 27 times
C. 9 times
D. 6 times

Solutions

Step: 1

Let r and h be the radius and height of the cylinder, respectively.

Step: 2

Volume of the cylinder = πr²h

[Formula.]

Step: 3

The height of the cylinder, after increasing it by 3 times is 3h.

Step: 4

Volume of the cylinder after increasing its height = π × r² × 3h

[Substitute h = 3h.]

Step: 5

= 3πr²h

[Simplify.]

Step: 6

= 3 × original volume of the cylinder

Step: 7

So, the volume of the cylinder becomes 3 times the original volume.

Correct Answer is : 3 times

Q10Find the volume of a cylinder with a base area of 8 square inches and height 5 inches.

A. 40 in.³
B. 3 in.³
C. 13 in.³
D. 8 in.³

Solutions

Step: 1

Volume of a cylinder = base area × height of the cylinder

Step: 2

= 8 in.² × 5 in.

[Substitute the values.]

Step: 3

= 40 in.³

[Multiply.]

Step: 4

So, the volume of the cylinder is 40 in.³.

Correct Answer is : 40 in.³

Q11Find the volume of a cylinder whose radius is 4 units and height is 14 units. [Use π = 227]

A. 4928 cubic units
B. 32 cubic units
C. 704 cubic units
D. 176 cubic units

Solutions

Step: 1

The formula for the volume of a cylinder is πr²h, where r is the radius of its base and h is its height.

Step: 2

Volume of the cylinder = π × 4² × 14

[Substitute the values of the base radius and the height.]

Step: 3

= 227 × 16 × 14

[Substitute π = 227.]

Step: 4

= 49287

[Multiply the numbers in the numerator.]

Step: 5

= 704

[Divide.]

Step: 6

So, the volume of the cylinder is 704 cubic units.

Correct Answer is : 704 cubic units

Q12Johnny made a cylinder using cardboard. What is the volume of the cylinder, if its base radius is 2 cm and height is 8 cm?

A. 48π cm³
B. 32π cm³
C. 24π cm³
D. 40π cm³

Solutions

Step: 1

The volume of a cylinder = πr²h

[Formula.]

Step: 2

= π × 2² × 8

[Substitute r = 2 and h = 8.]

Step: 3

= 32π cm ³

[Simplify.]

Step: 4

So, the volume of the cylinder that Johnny made is 32π cm ³.

Correct Answer is : 32π cm³

Solved Examples and Worksheet for Volume of Cylinders

Related Worksheet

Related Topic

HighSchool Math