Lesson Worksheet: Volumes of Rectangular Prisms and Cubes Mathematics • 6th Grade

In this worksheet, we will practice calculating volumes of rectangular prisms and cubes given their dimensions and solving problems including real-life situations.

Q1:

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

Q2:

A carton of juice is a rectangular prism 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?

Q3:

A rectangular-prism-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 meters.

Q4:

Find the area of the base of a rectangular prism that has a volume of 15,708 cm3 and a height of 17 cm.

  • A1924 cm2
  • B267,036 cm2
  • C924 cm2

Q5:

Find the length of a rectangular prism that has a volume of 10,868 cm3, a width of 11 cm, and a height of 19 cm.

Q6:

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 meters, the total volume of the bricks used.

Q7:

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

Q8:

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

Q9:

A rectangular-prism-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.

Q10:

A rectangular prism-shaped container has a square base with side lengths of 20 cm. If 2 liters of water are poured into the container, determine the height the water will reach.

Q11:

The height of a square-based rectangular prism is 6 cm. Given that its total edge length is 88 cm, find its volume.

  • A192 cm3
  • B384 cm3
  • C171 cm3
  • D512 cm3

Q12:

Which of the following describes how the volume of a rectangular prism is affected after doubling all three dimensions?

  • A𝑉=6𝑉newold
  • B𝑉=𝑉newold
  • C𝑉=2𝑉newold
  • D𝑉=4𝑉newold
  • E𝑉=8𝑉newold

Q13:

Anthony bought a big carton of milk as shown. He drinks 500 cubic centimeters of milk every day. How many days will it take him to drink all the milk?

Q14:

Fuel is stored in a rectangular-prism-shaped container that has length 31 cm, width 28 cm, and height 51 cm. The level of the fuel reaches 13 of the height. Given that the price of one liter of fuel is 1.60 LE, calculate the price of the fuel in the container to the nearest piaster.

Q15:

A cuboid container has length 34 cm, width 21 cm, and height 27 cm. If fuel fills one-third of the container, what is the volume of the fuel?

Q16:

A rectangular prism-shaped container has a base with dimensions 13 cm and 29 cm. It contains 8.9 liters of water. Find, to the nearest hundredth, the height of the water in the container.

Q17:

A rectangular-prism-shaped tin with dimensions 17 cm, 5 cm, and 25 cm is filled with honey. If the price of one liter of honey is 8 LE, how much does the honey in the tin cost?

Q18:

Sophia needs 225 cubic meters of storage space for her furniture. The space available at a storage company has a length of 12 meters, width of 10 meters, and height of 2 meters. Is the space large enough for Sophia’s furniture?

  • AYes
  • BNo

Q19:

A cubic glass tank has an inner edge length of 32 cm and is partly filled with water. After a metal disk is placed in the tank, the water level rises by 2 cm. What is the volume of the disk?

Q20:

A rectangular playground measuring 40 m by 30 m needs to be covered with sand. The sand is being carried by 2 identical trucks with inner dimensions of 5 m, 3 m, and 92 cm.

First, calculate the total volume of the sand. Then, find the thickness, in centimeters, of the sand on the playground.

  • AVolume of sand: 2,760 m, thickness: 86.957 cm
  • BVolume of sand: 27.6 m, thickness: 2.3 cm
  • CVolume of sand: 1,200 m, thickness: 92 cm
  • DVolume of sand: 1,380 m, thickness: 115 cm

Q21:

Given that 405 cm3 of water is poured into a rectangular-prism-shaped vessel with a square base whose side length is 9 cm, find the height of the water in the vessel.

Q22:

The sum of the edges of a rectangular prism is 84 cm. If its length is 9 cm, and its width is 8 cm, determine its volume.

Q23:

48 L of molasses is going to be equally divided between 6 tins. The tins have a rectangular base with length 16 cm and width 10 cm. Find the height of the molasses in each tin.

Q24:

A truck is carrying sand in a container with inner dimensions of 3.5 m, 1.6 m, and 2 m. If one cubic metre of sand costs 6.25 LE, what is the cost of the sand in the truck?

Q25:

A large cube of cheese with edges of length 40 cm is going to be divided into small cubes with edges of length 5 cm. How many small cubes will there be?

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