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

Tim Burnham

A rectangular prism-shaped swimming pool has a base with dimensions of 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 water in cubic metres.

02:35

Video Transcript

A rectangular prism-shaped swimming pool has a base with dimensions of sixty-seven metres and thirty-two metres and a height of three metres. Water fills the pool up to a height of twenty-seven 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 thirty-two metres, the length is sixty-seven metres, and the height is three metres. And when we add the water, it doesn’t quite fill the pool; it leaves a twenty-seven 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 thirty-two metres; it still got the same length of sixty-seven metres. But the height isn’t quite as big as three metres. It’s the three metres take away the twenty-seven 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 twenty-seven 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 hundred centimetres. So to convert those centimetres into metres, I’m gonna need to divide it by a hundred. And twenty-seven divided by a hundred is nought point two seven. So twenty-seven centimetres is nought point two seven metres. And three metres minus nought point two seven metres is two point seven three metres. So the depth of the water is two point seven three 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 sixty-seven metres, the width is thirty-two metres, and the height is two point seven three metres. When I put those into my calculator, I get five thousand eight hundred and fifty-three point one two. 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 five thousand eight hundred and fifty-three point one two cubic metres.