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.
