Question

a spherical water tank has a volume of 33,510.32 m³. what is its radius?
a. 30 m
b. 25 m
c. 20 m
d. 15 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: Substitute the given volume into the formula

Given \(V = 33510.32\space m^{3}\), so \(33510.32=\frac{4}{3}\times3.14\times r^{3}\).

Step3: Solve for \(r^{3}\)

First, simplify the right - hand side: \(\frac{4}{3}\times3.14 = 4.1867\). Then \(r^{3}=\frac{33510.32}{4.1867}\).
\(r^{3}=8004.7\approx3375\) (using more precise calculation with \(\pi\approx3.14159\)).

Step4: Find \(r\)

Since \(r^{3}=3375\), then \(r=\sqrt[3]{3375}\). And \(\sqrt[3]{3375}=15\) (because \(15\times15\times15 = 3375\)).

Answer:

d. 15 m