# Video: Finding the Volume of a Cuboid in a Real-World Context

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 27 cm from the brim of the pool. Find the volume of water in cubic metres.

02:34

### Video Transcript

A rectangular prism-shaped swimming pool has a base with dimensions of 67 metres and 32 metres and a height of three metres. Water fills the pool up to a height of 27 centimetres from the brim of the pool. Find the volume of water in cubic metres.

Right then, let’s start with a little sketch of the rectangular prism-shaped swimming pool. Now it’s not a scale; the width is 32 metres, the length is 67 metres, and the height is three metres. And when we add the water, it doesn’t quite fill the pool; it leaves a 27 centimetres gap at the top. And when we look at the water, we can see we’ve got a different rectangular prism shape. So it still got the same width of 32 metres; it still got the same length of 67 metres. But the height isn’t quite as big as three metres. It’s the three metres take away the 27 centimetres.

Now our question has asked us to find the volume of the water in cubic metres. So I’m gonna need to convert this height whatever it is into metres. So I can’t do a calculation of three metres minus 27 centimetres unless they’re in the same unit. So I’m gonna convert centimetres into metres so I can work purely in metres. Now one metre contains a 100 centimetres. So to convert those centimetres into metres, I’m gonna need to divide it by a 100. And 27 divided by a 100 is 0.27. So 27 centimetres is 0.27 metres. And three metres minus 0.27 metres is 2.73 metres. So the depth of the water is 2.73 metres.

Hopefully you recall that the volume of a rectangular prism is equal to its length times its width times its height. Now we have those numbers that we can work that out for the water. Well the length is 67 metres, the width is 32 metres, and the height is 2.73 metres. When I put those into my calculator, I get 5853.12. Now because our units of length were metres. Metres times metres times metres gives us metres cubed or cubic metres. So the answer is the volume of water in cubic metres is 5853.12 cubic metres.