Volume of Prisms and Cylinders Worksheet

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 ft3 b. 324,000 ft3 c. 90,000 ft3 d. 57,000 ft3

Solution:

Length of the water tank = 90 ft.

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 l = 90, w = 60 and h = 30.]

= 162000 ft3
[Multiply 90, 60 and 30.]

Volume of water in the tank is 162000 ft3.

2.
The volume of a rectangular prism is 1050 cm3. 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

Solution:

Volume of the prism = length × width × height.

V = l × w × h
[Write an equation.]

l = Vw × h

= 1050(7 × 10)
[Substitute V = 1050, w = 10, and h = 7.]

= 1050 / 70
[Multiply 10 and 7.]

= 15 cm
[Divide 1050 by 70.]

The length of the prism is 15 cm.

3.
The base area of a rectangular prism is 20 cm2. What is the height of the prism, if the volume of the prism is 80 cm3?
 a. 5 cm b. 6 cm c. 3 cm d. 4 cm

Solution:

Volume of a prism = base area × height.

The height of the prism = volume / basearea .

= 80 / 20
[Substitute volume = 80 and height = 20.]

= 4
[Divide 80 by 20.]

The height of the prism is 4 cm.

4.
What is the volume of the prism?
(Volume =base area × h)

 a. 70 cm3 b. 50 cm3 c. 60 cm3 d. None of the above

Solution:

From the figure, the length of the rectangular prism l = 5 cm, the width of the rectangular prism w = 3 cm, and the height of the rectangular prism h = 4 cm.

The base area of the rectangular prism B = length × width = 5 × 3
[Substitute values.]

= 15 cm2

The volume of the rectangular prism = base area × height = 15 × 4
[Substitute B = 15 and h = 4.]

= 60 cm3
[Multiply 15 and 4.]

The volume of the rectangular prism is 60 cm3.

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

Solution:

From the figure, the length of the rectangular prism is 4x, width is 2x and height is 3x.

= 4x × 2x × 3x
Volume of the rectangular prism = length × width × height
[Substitute the values.]

= 24x3
[Multiply the coefficients and add the exponents of x.].

The volume of the rectangular prism is 24 x3.

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 = πr2h)
 a. 60$\pi$ ft3 b. 54$\pi$ ft3 c. 48$\pi$ ft3 d. none of these

Solution:

The volume of a cylinder = πr2h
[Formula.]

= π × 32 × 6
[Substitute r = 3 and h = 6.]

= 54π ft 3
[Simplify.]

So, the volume of the cylinder that Johnny made is 54π ft 3.

7.
Bill wants to build a rectangular tub that is 2 ft high and holds 180 ft3 of water. What is the base area of the tub?
 a. 100 ft2 b. 90 ft2 c. 80 ft2 d. 190 ft2

Solution:

The volume of the tub is 180 ft3 and the height of the tub is 2 ft.
[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 = Volume / Height.

B = 180 / 2
[Substitute volume = 180 and height = 2.]

B = 90 ft2
[Divide 180 by 2.]

The base area of the hot tub is 90 ft2.

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.

Solution:

Let the height of the cylinder be h.

Volume of a cylinder, V = π r2 h.
[Formula.]

904 = 3.14 × 25 × h
[Substitute the values.]

904 = 78.5 h
[Simplify.]

h = 904 / 78.5= 11.51 = 12 in.
[To the nearest ten.]

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

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

Solution:

Volume of a cylinder = area of the base × height
[Formula.]

Approximate area of the base of the cylindrical glass = πr2 = 3 × 2 × 2 = 12 in.2
[Use π = 3.]

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

Solution:

Length of the box = 11.2 in. 11 in.
Height of the box = 14.7 in. 15 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.3
[Substitute the values.]