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

Mar 10, 2017

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: $\pi {r}^{2} h$ 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 =$\frac{x}{3}$ feet. We are also told that its length is 6 feet.

$\therefore$ the volume of the rectangular pool, $\left({V}_{r}\right) = 6 \times x \times \frac{x}{3}$

${V}_{r} = 2 {x}^{2}$ cubic feet

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

$\therefore$ the volume of the circular pool, $\left({V}_{c}\right) = \pi {x}^{2} \cdot 2$ cubic feet

${V}_{c} = 2 \pi {x}^{2}$ cubic feet

Hence the ratio of the volumes $= {V}_{c} / {V}_{r}$

$= \frac{2 \pi {x}^{2}}{2 {x}^{2}}$

$= \pi$ [or $\pi$:1]