Question

1. a soccer ball is modeled as a sphere with a radius of 11 cm. what is the volume of the ball in terms of π?

a. 4000π cm³
b. 1234π cm³
c. \frac{5324}{3}π cm³
d. \frac{1331}{3}π cm³

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given radius into the formula

Given \(r = 11\ \text{cm}\), then \(V=\frac{4}{3}\pi\times(11)^{3}\).

Step3: Calculate \(11^{3}\)

\(11^{3}=11\times11\times11 = 1331\).

Step4: Multiply by \(\frac{4}{3}\)

\(V=\frac{4\times1331}{3}\pi=\frac{5324}{3}\pi\ \text{cm}^3\).

Answer:

C. \(\frac{5324}{3}\pi\ \text{cm}^3\)