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

Answer:

$D.\ 3328\ ft^3$

Step-by-step 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