Worksheet: Volume of a Rectangular Prism

In this worksheet, we will practice calculating the volume of a rectangular prism given the lengths of its 3 dimensions to solve problems including real-life situations.

Q1:

Complete the formula for the volume of a cuboid: × × .

  • Aheight, base area, length
  • Blength, width, base area
  • Cbase area, width, height
  • Dlength, width, height

Q2:

Find the volume of the cuboid.

Q3:

Olympic gold medal winner Ian Thorp competes in a pool with required dimensions 25 by 50 by 2 metres. What is the volume of the Olympic-sized pool?

Q4:

Which of these is equal to the volume of a cuboid?

  • Awidth × base area
  • Bheight × perimeter of the base
  • Clength × width + height
  • Dheight × base area

Q5:

If a cuboid has a height of 15 cm and a base with area 760 cm2, what is its volume?

Q6:

Determine the volume of a container that is 9 units long, 7 units wide, and 4 units high.

Q7:

A carton of juice is a cuboid with height 12 cm. Its base is a square with side length 5 cm. What is the volume of juice that will fill the carton?

Q8:

A cuboid-shaped swimming pool has a base of dimensions 67 m and 32 m and a height of 3 m. Water fills the pool up to a height of 27 cm from the brim of the pool. Find the volume of the water in cubic metres.

Q9:

Find the area of the base of a cuboid which has a volume of 15 708 cm3 and a height of 17 cm.

  • A 1 9 2 4 cm2
  • B 267 036 cm2
  • C 924 cm2

Q10:

Find the length of a cuboid which has a volume of 10 868 cm3, a width of 11 cm, and a height of 19 cm.

Q11:

Given that the volume of the smaller cube is 8 cubic feet, determine the volume of the larger cube.

Q12:

Cuboid 𝐴 has dimensions of 56 cm, 40 cm, and 34 cm. Cuboid 𝐵 has a base area of 2 904 cm2 and a height of 36 cm. Which cuboid is greater in volume?

  • A Cuboid 𝐵
  • B Cuboid 𝐴

Q13:

A cuboid has dimensions of 9 cm, 20 cm, and 7 cm. A second cuboid has a height of 16 cm and a base with area 60 cm2. Find the difference between the volumes of the two cuboids.

Q14:

A construction worker used 3 000 bricks to build a wall. The bricks had a length of 47 cm, a width of 27 cm, and a height of 16 cm. Calculate, in cubic metres, the total volume of the bricks used.

  • A 60 912 000 m3
  • B 20 304 m3
  • C 6.768 m3
  • D 60.912 m3

Q15:

A tank is a cuboid with dimensions 50 m, 24 m, and 19 m. What is the volume of water necessary to fill one third of the tank?

Q16:

A man needs to store 16 170 cm3 of rice in a container. He has one box which is a cuboid with dimensions of 35 cm, 22 cm, and 21 cm and another box which is a cube with length 22 cm. Which box should he use?

  • Athe cuboid
  • Bthe cube

Q17:

Complete the formula for the height of a cuboid: ÷ .

  • Avolume of cuboid, length
  • Bbase area, volume of cuboid
  • Cwidth, volume of cuboid
  • Dvolume of cuboid, base area

Q18:

Complete the formula for the base area of a cuboid: ÷ .

  • Avolume of cuboid, length
  • Bheight, volume of cuboid
  • Cwidth, volume of cuboid
  • Dvolume of cuboid, height

Q19:

Find the height of a cuboid which has a volume of 1 152 cm3 and a base area of 128 cm2.

Q20:

Find the width and the height of a cuboid whose volume is 15 360 cm3, length is 40 cm, and base area is 960 cm2.

  • A width: 384 cm, height: 16 cm
  • B width: 16 cm, height: 24 cm
  • C width: 16 cm, height: 384 cm
  • Dwidth: 24 cm, height: 16 cm

Q21:

The tank shown contains 3 496 cm3 of water. Find the current height of the water in the tank, and calculate the volume of water that needs to be added to fill the tank.

  • AHeight of water: 10.86 cm. Volume to add: 1 372.18 cm3
  • BHeight of water: 14 cm. Volume to add: 3 059 cm3
  • CHeight of water: 13.14 cm. Volume to add: 375.82 cm3
  • DHeight of water: 8 cm. Volume to add: 2 622 cm3

Q22:

A cuboid-shaped swimming pool has a base of length 64 m and a width of 56 m. If 28 672 m3 of water fills it completely, determine its depth.

Q23:

A cuboid-shaped container has a square base with side lengths of 20 cm. If 2 litres of water are poured into the container, determine the height the water would reach.

Q24:

Find the dimensions of the box described: the length is 3 inches longer than the width, the width is 2 inches longer than the height, and the volume is 120 cubic inches.

  • A 5 in by 10 in by 15 in
  • B 5 in by 7 in by 8 in
  • C 4 in by 6 in by 9 in
  • D 3 in by 5 in by 8 in
  • E 6 in by 8 in by 9 in

Q25:

Find the dimensions of a box with a length three times its height, a height one inch less than its width, and a volume of 108 cubic inches.

  • A 2 in by 3 in by 6 in
  • B 3 in by 4 in by 6 in
  • C 3 in by 4 in by 5 in
  • D 3 in by 4 in by 9 in
  • E 4 in by 5 in by 12 in

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