Question

a spherical water tank holds 11,500 ft³ of water. what is the diameter of the tank? (hint: $v = \frac{\pi}{6}d^3$)

the diameter is \\(\square\\) ft.
(simplify your answer. round to two decimal places as needed.)

Explanation:

Step1: Substitute the value of \( V \) into the formula

Given \( V=\frac{\pi}{6}d^{3}\) and \( V = 11500\), we have \(11500=\frac{\pi}{6}d^{3}\).

Step2: Solve for \( d^{3}\)

Multiply both sides by \(\frac{6}{\pi}\): \(d^{3}=\frac{11500\times6}{\pi}\).

Step3: Calculate the value of \( d^{3}\)

\(d^{3}=\frac{69000}{\pi}\approx\frac{69000}{3.14159}\approx21963.49\).

Step4: Solve for \( d\)

Take the cube - root of both sides: \(d=\sqrt[3]{21963.49}\approx28.90\).

Answer:

\(28.90\)