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ANSWER

12 ft

EXPLANATION

The volume of a cylinder is calculated using the formula

[tex]V=\pi {r}^{2} h[/tex]

From the question, the volume was given as 540π ft³ .

The height is given as 15 ft.

We substitute the values to obtain:

[tex]540\pi=\pi {r}^{2} \times 15[/tex]

This implies that;

[tex] {r}^{2} = \frac{540\pi}{15\pi} [/tex]

We simplify to get;

[tex] {r}^{2}=36[/tex]

Take positive square root to obtain:

[tex]r = \sqrt{36} [/tex]

[tex]r = 6ft[/tex]

The diameter is twice the radius.

Hence the diameter is 12ft

mixter17

Hello!

The answer is:

The diameter of the cylinder is equal to 12 feet.

Why?

To find the diameter of the cylinder we need to use the formula to calculate its volume.

So,  we have:

[tex]Volume=\pi *r^{2}*h[/tex]

We are given the following dimensions of the cylinder:

[tex]Volume=540\pift^{3}\\\\Height=15ft^{3}[/tex]

Now, using substituting and isolating the radius in order to find the diameter, we have:

[tex]Volume=\pi *r^{2}*h\\\\r^{2}=\frac{Volume}{\pi *h} \\\\r=\sqrt{\frac{Volume}{\pi *h} }[/tex]

Therefore, we have:

[tex]r=\sqrt{\frac{Volume}{\pi *h}}\\\\r=\sqrt{\frac{540\pi ft^{3}}{\pi *15ft}}\\\\r=\sqrt{36ft^{2} }=6ft[/tex]

We know the radius, then, calculating the diameter we have:

[tex]diameter=2*radius=2*6ft=12ft[/tex]

Hence, we have that the diameter of the cylinder is equal to 12 feet.

Have a nice day!

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