Question

what is the volume of this sphere?
round your answer to the nearest hundredth.
4 cm
cubic centimeters

Explanation:

Step1: Write 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 radius value into the formula

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

Step3: Calculate the numerical value

Using \( \pi\approx3.14159\), we have \( V=\frac{256}{3}\times3.14159\).
\( \frac{256}{3}\times3.14159=\frac{256\times3.14159}{3}\).
\(256\times3.14159 = 804.24704\).
\( V=\frac{804.24704}{3}=268.0823467\).

Answer:

\(268.08\)