Question

1. a spherical water tank has a volume of 33,510.32 m³. what is its radius?

a. 25 m
b. 30 m
c. 15 m
d. 20 m

Explanation:

Step1: Recall the formula for the volume of a sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\), where \(V\) is the volume and \(r\) is the radius.

Step2: Substitute the given volume into the formula

Given \(V = 33510.32\space m^{3}\) and \(\pi\approx3.14\), we have the equation \(33510.32=\frac{4}{3}\times3.14\times r^{3}\).

First, simplify the right - hand side: \(\frac{4}{3}\times3.14 = 4.1866\cdots\). So the equation becomes \(33510.32 = 4.1866\cdots\times r^{3}\).

Then, solve for \(r^{3}\): \(r^{3}=\frac{33510.32}{4.1866\cdots}\).

\(r^{3}=8000\).

Step3: Find the radius

Take the cube root of both sides. Since \(20\times20\times20 = 8000\), \(r = 20\space m\).

Answer:

d. \(20\space m\)