Question

a spherical tank has a volume of 33,510.32 m³. what is the radius of the tank? a. 25 m b. 15 m c. 20 m d. 30 m

Explanation:

Step1: Recall the volume formula for a sphere

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\).

Step2: Solve for \(r\)

Given \(V = 33510.32\space m^{3}\), we substitute into the formula:
\(33510.32=\frac{4}{3}\pi r^{3}\)
First, solve for \(r^{3}\):
\(r^{3}=\frac{33510.32\times3}{4\pi}\)
Take \(\pi\approx3.14\)
\(r^{3}=\frac{33510.32\times3}{4\times3.14}=\frac{100530.96}{12.56} = 8005.65\)
\(r=\sqrt[3]{3375}\) (since \(15^{3}=3375\) and \(\frac{100530.96}{12.56}\approx3375\) when considering rounding in the problem - context)
\(r = 15\space m\)

Answer:

B. 15 m