Volume of Prisms and Cylinders Worksheet

**Page 1**

1.

A water tank is 90 ft long and 60 ft wide. What is the volume of the water in the tank, if the depth of water is 30 ft?

a. | 162,000 ft ^{3} | ||

b. | 324,000 ft ^{3} | ||

c. | 90,000 ft ^{3} | ||

d. | 57,000 ft ^{3} |

Width of the water tank = 60 ft.

The height of the water level = 30 ft.

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

= 90 × 60 × 30

[Substitute

= 162000 ft

[Multiply 90, 60 and 30.]

Volume of water in the tank is 162000 ft

Correct answer : (1)

2.

The volume of a rectangular prism is 1050 cm^{3}. If the width of the prism is 10 cm and the height is 7 cm, then find the length of the rectangular prism.

a. | 20 cm | ||

b. | 15 cm | ||

c. | 25 cm | ||

d. | None of the above |

[Write an equation.]

=

[Substitute

=

[Multiply 10 and 7.]

= 15 cm

[Divide 1050 by 70.]

The length of the prism is 15 cm.

Correct answer : (2)

3.

The base area of a rectangular prism is 20 cm^{2}. What is the height of the prism, if the volume of the prism is 80 cm^{3}?

a. | 5 cm | ||

b. | 6 cm | ||

c. | 3 cm | ||

d. | 4 cm |

The height of the prism =

=

[Substitute volume = 80 and height = 20.]

= 4

[Divide 80 by 20.]

The height of the prism is 4 cm.

Correct answer : (4)

4.

What is the volume of the prism?

(Volume =base area × h)

(Volume =base area × h)

a. | 70 cm ^{3} | ||

b. | 50 cm ^{3} | ||

c. | 60 cm ^{3} | ||

d. | None of the above |

The base area of the rectangular prism

[Substitute values.]

= 15 cm

The volume of the rectangular prism = base area × height = 15 × 4

[Substitute

= 60 cm

[Multiply 15 and 4.]

The volume of the rectangular prism is 60 cm

Correct answer : (3)

5.

Which expression represents the volume of the rectangular prism?

a. | 24$x$ ^{2} | ||

b. | 24$x$ ^{3} | ||

c. | 16$x$ ^{3} | ||

d. | None of the above |

= 4

Volume of the rectangular prism = length × width × height

[Substitute the values.]

= 24

[Multiply the coefficients and add the exponents of

The volume of the rectangular prism is 24

Correct answer : (2)

6.

Johnny made a cylinder using cardboard paper. What is the volume of the cylinder, if its base radius is 3 ft and height is 6 ft?

(Volume = πr^{2}h)

(Volume = πr

a. | 60$\pi $ ft ^{3} | ||

b. | 54$\pi $ ft ^{3} | ||

c. | 48$\pi $ ft ^{3} | ||

d. | none of these |

[Formula.]

=

[Substitute

= 54

[Simplify.]

So, the volume of the cylinder that Johnny made is 54

Correct answer : (2)

7.

Bill wants to build a rectangular tub that is 2 ft high and holds 180 ft^{3} of water. What is the base area of the tub?

a. | 100 ft ^{2} | ||

b. | 90 ft ^{2} | ||

c. | 80 ft ^{2} | ||

d. | 190 ft ^{2} |

[Capacity of the tub is nothing but the volume of the tub.]

Let 'B' be the base area of the hot tub.

Volume of the rectangular tub = Base area × Height of the tub.

So, base area of the tub =

B =

[Substitute volume = 180 and height = 2.]

B = 90 ft

[Divide 180 by 2.]

The base area of the hot tub is 90 ft

Correct answer : (2)

8.

The volume of a cylinder is 904 in.^{3}. and its radius is 5 in. Find the height of the cylinder to the nearest ten.

a. | 11 in. | ||

b. | 12.51 in. | ||

c. | 12 in. | ||

d. | 11.51 in. |

Volume of a cylinder, V = π

[Formula.]

904 = 3.14 × 25 ×

[Substitute the values.]

904 = 78.5

[Simplify.]

[To the nearest ten.]

So, the height of the cylinder to the nearest ten is 12 in.

Correct answer : (3)

9.

Julia prepared a glass of pineapple juice. The shape of the glass is shown below. Estimate the volume of the glass. Round to the nearest whole number.

a. | 112 in. ^{2} | ||

b. | 140 in. ^{3} | ||

c. | 72 in. ^{3} | ||

d. | 56 in. ^{3} |

[Formula.]

Approximate area of the base of the cylindrical glass =

[Use π = 3.]

Approximate volume of the cylindrical glass = 12 × 6 = 72 in.

Correct answer : (3)

10.

A wooden box is 5 in. wide, 11.2 in. long, and 14.7 in. high. Find the approximate volume of the box.

a. | 750 in. ^{3} | ||

b. | 880 in. ^{3} | ||

c. | 825 in. ^{3} | ||

d. | 725 in. ^{3} |

Height of the box = 14.7 in.

Width of the box = 5 in.

Volume of a box = length × height × width

[Formula.]

Approximate volume of the box = 11 × 15 × 5 = 825 in.

[Substitute the values.]

Correct answer : (3)