Question

A baby pool is shaped like a short, wide cylinder and holds 52 ft3 of water. A medium pool measures 4 times the height and width of the baby pool. How much water will the medium pool hold? A. 1045 ft3 B. 2812 ft3 C. 2920 ft3 D. 3328 ft3

Answer 1

`D.\ 3328\ ft^3`

Explanation:

Given

Volume of baby pool = 52ft³

Required

Determine the volume of the medium pool

Volume of a cylinder is calculated as:

`V = \pi r^2h`

Hence, the volume of the baby pool is:

`\pi r^2h = 52`

where r and h are the radius and height of the baby pool

Represent the height and radius of the medium pool as H and R

From the given parameters in the question

`H = 4 * h` and
`R = 4 * r`

`H = 4 h` and
`R = 4 r`

The volume of the medium cylinder is calculated as

`Volume = \pi R^2H`

Substitute 4h for H and 4r for R

`Volume = \pi (4r)^2(4h)`

Open bracket

`Volume = \pi (4r) * (4r) * (4h)`

`Volume = \pi 16r^2 * (4h)`

`Volume = \pi 16r^2 * 4h`

Collect like terms

`Volume = \pi r^2 * h * 4 * 16`

`Volume = \pi r^2 h * 64`

Recall that
`\pi r^2h = 52`

So, the expression becomes

`Volume = 52 * 64`

`Volume = 3328`

Hence, the medium pool can hold
`3328ft^3` of water