WORD PROBLEMS ON VOLUME OF 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.