Question

1. if you have a sphere with a radius of 4 cm, what is its volume?

a. 252.14 cm³
b. 201.06 cm³
c. 301.44 cm³
d. 268.08 cm³

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given radius into the formula

Given \(r = 4\ \text{cm}\), we substitute into the formula: \(V=\frac{4}{3}\times\pi\times(4)^{3}\).
First, calculate \((4)^{3}=4\times4\times4 = 64\). Then the formula becomes \(V=\frac{4}{3}\times\pi\times64=\frac{256\pi}{3}\).

Step3: Calculate the numerical value

Taking \(\pi\approx3.14\), we have \(V=\frac{256\times3.14}{3}\).
\(256\times3.14 = 803.84\). Then \(V=\frac{803.84}{3}\approx301.44\ \text{cm}^3\).

Answer:

C. \(301.44\ \text{cm}^3\)