Question

a cylinder has a radius of 2 cm and a height of 3 cm. what is the volume of a sphere with the same radius?
a. 33.51 cubic centimeters
b. 21.35 cubic centimeters
c. 12 cubic centimeters
d. 50 cubic centimeters

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 given radius into the formula

Given \(r = 2\) cm. Substitute \(r = 2\) into \(V=\frac{4}{3}\pi r^{3}\), we get \(V=\frac{4}{3}\pi(2)^{3}\).

Step3: Calculate the value

First, calculate \((2)^{3}=8\). Then \(V=\frac{4}{3}\pi\times8=\frac{32}{3}\pi\). Using \(\pi\approx3.14\), \(V=\frac{32\times3.14}{3}=\frac{100.48}{3}\approx33.51\) cubic centimeters.

Answer:

A. 33.51 cubic centimeters