Question

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. 1234π cm³
b. 4000π cm³
c. 1331/3 π cm³
d. 5324/3 π cm³

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given radius into the formula

Given $r = 11$ cm. Substitute $r=11$ into the formula: $V=\frac{4}{3}\pi\times(11)^3$.

Step3: Calculate $11^3$

$11^3=11\times11\times11 = 1331$.

Step4: Calculate the value of $\frac{4}{3}\times1331$

$\frac{4}{3}\times1331=\frac{4\times1331}{3}=\frac{5324}{3}$.

Step5: Get the volume of the sphere

So, $V = \frac{5324}{3}\pi\text{ cm}^3$.

Answer:

D. $\frac{5324}{3}\pi \text{ cm}^3$