Question

the volume of a sphere with a radius of r is given by \\( \frac { 4 } { 3 } \pi r ^ { 3 } \\). what is the approximate value of \\( \pi \\)?
a. 3.14
b. 3.15
c. 2.72
d. 1.12

what is the volume of a sphere with a radius of 3 inches?
a. 121.3 cubic inches.
b. 113.1 cubic inches
c. 100 cubic inches
d. 150 cubic inches

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the value of \(r = 3\) into the formula

When \(r = 3\), we have \(V=\frac{4}{3}\pi(3)^{3}\). First, calculate \((3)^{3}=3\times3\times3 = 27\). Then, \(V=\frac{4}{3}\pi\times27\). Since \(\frac{4}{3}\times27=4\times9 = 36\), so \(V = 36\pi\).

Step3: Approximate the value of \(\pi\)

Taking \(\pi\approx3.14\), then \(V\approx36\times3.14=113.04\approx113.1\) (cubic inches).

Answer:

b. 113.1 cubic inches