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In this lesson, we will learn how to calculate 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: × × .

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?

Q5:

If a cuboid has a height of 15 cm and a base with area 760 cm^{2}, 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 cm^{3} and a height of 17 cm.

Q10:

Find the length of a cuboid which has a volume of 10 868 cm^{3}, 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 cm^{2} and a height of 36 cm. Which cuboid is greater in volume?

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 cm^{2}. 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.

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 cm^{3} 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?

Q17:

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

Q18:

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

Q19:

Find the height of a cuboid which has a volume of 1 152 cm^{3} and a base area of 128 cm^{2}.

Q20:

Find the width and the height of a cuboid whose volume is 15 360 cm^{3}, length is 40 cm, and base area is 960 cm^{2}.

Q21:

The tank shown contains 3 496 cm^{3} 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.

Q22:

A cuboid-shaped swimming pool has a base of length 64 m and a width of 56 m. If 28 672 m^{3} 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.

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.

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