Question

a spherical water tank holds 8,500 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 given volume into the formula

Given \( V=\frac{\pi}{6}d^{3}\) and \( V = 8500\), we substitute \(V\) into the formula: \(8500=\frac{\pi}{6}d^{3}\).

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

Multiply both sides of the equation by \(\frac{6}{\pi}\): \(d^{3}=\frac{8500\times6}{\pi}\).
Calculate \(\frac{8500\times6}{\pi}=\frac{51000}{\pi}\approx\frac{51000}{3.14159}\approx16233.23\).

Step3: Solve for \(d\)

Take the cube - root of both sides: \(d=\sqrt[3]{16233.23}\).
Using a calculator, \(d\approx25.32\).

Answer:

\(25.32\)