Video: Finding the Height of a Rectangular Prism given Its Volume and Two of Its Dimensions to Solve a Word Problem

A rectangular tank is 90 cm wide and 100 cm long. It can hold up to 810 liters of water when full. If it is filled to one-third of its height, determine the height of the water in centimeters.

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Video Transcript

A rectangular tank is 90 centimeters wide and 100 centimeters long. It can hold up to 810 litres of water when full. If it is filled to one-third of its height, determine the height of the water in centimeters.

Let’s consider the rectangular tank as shown in the diagram. We are told that it is 100 centimeters long and 90 centimeters wide. The total volume of the tank is 810 litres. We are told in the question that the tank is filled to one-third of its height. We can therefore calculate the amount of water in the tank by working out one-third of 810. This is the same as multiplying one-third by 810.

Multiplying by one-third is the same as dividing by three. So, we need to divide 810 by three. 81 divided by three is equal to 27. Therefore, 810 divided by three is 270. When the tank is one-third full, there is 270 litres of water in the tank. One litre is equal to 1000 millilitres. Therefore, one litre is also equal to 1000 centimeters cubed. Multiplying 270 by 1000 gives us 270000. Therefore, the volume of water in the tank in centimeters cubed is 270000.

We can calculate the volume of any cuboid or rectangular prism by multiplying the length by the width by the height. In this case, we have 100 multiplied by 90 multiplied by ℎ. This is equal to 270000. 90 multiplied by 100 is 9000. So, 9000 multiplied by ℎ is equal to 270000. Dividing both sides of this equation by 9000 gives us ℎ is equal to 270000 divided by 9000. Both the numerator and denominator are divisible by 1000. This cancels three of the zeroes. So, ℎ is equal to 270 divided by nine. 27 divided by nine is equal to three. So, 270 divided by nine equals 30. When the rectangular tank is filled to one-third of its height, the height of water in centimeters is 30 centimeters.

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