WORD PROBLEMS ON VOLUME OF A RECTANGULAR PRISM

Problem 1 :

The bottom of a tank measures 50 m × 40 m. Find its depth if it contains 4000 m³ of water.

Solution :

Length = 50 m, Breadth = 40 m, Volume = 4000 m³

Volume of rectangle = length × breadth × height

4000 = 50 ⋅ 40 ⋅ h

4000 = 2000 ⋅ h

h = 4000/2000

h = 2 m

So, depth of water tank is 2 m.

Problem 2 :

The volume of a rectangular prism whose length, breadth and height are 2a, 3a and 4a is.

a) 24a²        b) 24a³        c) 12a³      d) none of these

Solution :

Measures of rectangular prism,

Length = 2a, width = 3a and height = 4a

Volume of rectangular prism = length x width x height.

= 2a ⋅ 3a ⋅ 4a

= 24a³

Problem 3 :

The surface area of a cuboid is 1372 sq. cm. If its dimensions are in the ratio of 4 : 2 : 1, find the volume.

Solution :

Surface area of rectangular prism = 1372 sq.cm

length = 4x, width = 2x and height = x

2(4x ⋅ 2x + 2x ⋅ x + x ⋅ 4x) = 1372

2(8x² + 2x² + 4x²) = 1372

2(14x²) = 1372 

x² = 49

x = 7

Volume = 4x(2x)(x)

= 8x³

= 8(7)³

= 2744 cm³

Problem 4 :

The volume of a rectangular prism is 24 ft³, the height is 2, what are three possible measures for the length and width of the prism?

Solution :

Volume of rectangular prism = 24

length ⋅ width ⋅ height = 24

length ⋅ width ⋅ 2 = 24

length ⋅ width = 12

If length = 3, width = 4

If length = 2, width = 6

If length = 1, width = 12

Problem 5 :

A box of tissues has a length of 11.2 cm, a width of 11.2 cm and a height of 13 cm. What is the volume of the tissue box ?

Solution :

length = 11.2 cm, width = 11.2 cm and height = 13 cm

Volume of the box = length x width x height

= 11.2 x 11.2 x 13

= 1630.72 cm³

So, the volume of the box is 1630.72 cm³.

Problem 6 :

A terrarium is shaped like a rectangular prism. The prism is 25 1/2 inches long, 13 1 / 2 inches wide, and 16 inches deep. What is the volume of the terrarium?

Solution :

Length = 25   1/2 inches ==>  51/2

width = 13  1/2 inches ==> 27/2

height = 16 inches

Volume of terrarium = length x width x height

= (51/2) ⋅ (27/2) ⋅ 16

= 51 ⋅ 27 ⋅ 4

= 5508 cubic inches

Problem 7 :

A block of wood measures 4.5 inches by 3.5 inches by 7 inches. What is the volume of the block of wood?

Solution :

Length = 4.5 inches

width = 3.5 inches

height = 7 inches

Volume of black wood = length x width x height

= 4.5 x 3.5 x 7

= 110.25 cubic inches

Problem 8 :

A restaurant buys a freezer in the shape of a rectangular prism. The dimensions of the freezer are shown. What is the volume of the freezer?

Solution :

Length = 72  1/2 inches ==> 145/2

width = 24  1/2 inches ==> 49/2

height = 36 inches

Volume of black wood = length x width x height

= (145/2) (49/2) 36

= 145 x 49 x 9

= 63945 cubic inches

Problem 9 :

Rectangular prism A measures 6 inches by 4 inches by 5 inches. Rectangular prism B’s dimensions are twice those of prism A. Find the volume of each prism. How many times as great is prism B’s volume as prism A’s volume?

Solution :

Volume of prism A = length x width x height

= 6 x 4 x 5

= 120 cubic inches

Volume of prism B = 12 x 8 x 10

= 960 cubic inches

Volume of prism B / volume of prism A

= 960/120

= 8

So, volume of prism B is 8 times of prism A.

Problem 10 :

Leticia has a small paper weight in the shape of a rectangular prism. The dimensions of the paper weight are shown. What is the volume of the paper weight?

Solution :

Length = 4  1/4 cm ==> 17/4

width = 2  3/4 cm ==> 11/4

height = 5 cm

Volume of paper weight = (17/4) (11/4) 5

= (187 x 5)/16

= 935/16

= 58.43 cubic cm

Problem 11 :

The dimensions of a rectangular prism are 3 1/4 feet by 2 1/2 feet by 5 feet.

• Lee found the volume by multiplying 12 1/2 by 3 1/4
• Lola found the volume by multiplying 16 1/4 by 2 1/2

Who is correct? Explain.

Solution :

Length = 3  1/4 ==> 13/4

width = 2  1/2 ==> 5/2

height = 5 feet

volume of rectangular prism = (13/4)(5/2) 5

= 325/8

= 40.625 cubic feet

Volume of prims found by Lee :

= 12  1/2 x 3  1/4

= 25/2 x 13/4

= 325/8

= 40.625 cubic feet

Volume of prims found by Lola :

= 16  1/4 x 2  1/2

= 65/4 x 5/2

= 325/8

= 40.625 cubic feet

So, both are correct.