Answer:
[tex]D.\ 3328\ ft^3[/tex]
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:
[tex]V = \pi r^2h[/tex]
Hence, the volume of the baby pool is:
[tex]\pi r^2h = 52[/tex]
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
[tex]H = 4 * h[/tex] and [tex]R = 4 * r[/tex]
[tex]H = 4 h[/tex] and [tex]R = 4 r[/tex]
The volume of the medium cylinder is calculated as
[tex]Volume = \pi R^2H[/tex]
Substitute 4h for H and 4r for R
[tex]Volume = \pi (4r)^2(4h)[/tex]
Open bracket
[tex]Volume = \pi (4r) * (4r) * (4h)[/tex]
[tex]Volume = \pi 16r^2 * (4h)[/tex]
[tex]Volume = \pi 16r^2 * 4h[/tex]
Collect like terms
[tex]Volume = \pi r^2 * h * 4 * 16[/tex]
[tex]Volume = \pi r^2 h * 64[/tex]
Recall that [tex]\pi r^2h = 52[/tex]
So, the expression becomes
[tex]Volume = 52 * 64[/tex]
[tex]Volume = 3328[/tex]
Hence, the medium pool can hold [tex]3328ft^3[/tex] of water
