Question

Here we have two swimming pools. A rectangular pool is `6`ft long and a depth 1/3 of its width. A circular pool is `2`ft deep and has a diameter twice the width of the rectangular pool. What is the ratio of their volumes?

Answer 1

The ratio of the volumes of the pools is `pi`. Explanation below.

Explanation:

The pools are both regular 3 dimensional objects. The 'rectangular' pool is a cuboid and the 'circular' pool is a cylinder.

The volume of a cuboid is: length x width x depth

The volume of a cylinder is: `pir^2h` Where r is the radius and h the height (or depth in this case)

Let `x` be the width of the recangular pool in feet

We are told the the depth of the this pool is a third of its width =`x/3` feet. We are also told that its length is 6 feet.

`:.` the volume of the rectangular pool, `(V_r) = 6 xx x xx x/3`

`V_r = 2x^2` cubic feet

For the circular pool, we are told that its diameter is twice the width of the other, which is therefore `2x -> r=x` feet. We are also told that this pool is 2 ft deep.

`:.` the volume of the circular pool, `(V_c) = pi x^2 * 2` cubic feet

`V_c = 2pix^2` cubic feet

Hence the ratio of the volumes `=V_c/V_r`

`= (2pix^2)/(2x^2)`

`=pi` [or `pi`:1]