Question

what is the volume of a sphere with a radius of 6.4 in, rounded to the nearest tenth of a cubic inch?

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.

Step2: Substitute the value of the radius

Given \( r = 6.4 \) inches. Substitute \( r = 6.4 \) into the formula:
\( V=\frac{4}{3}\pi(6.4)^{3} \)
First, calculate \( (6.4)^{3}=6.4\times6.4\times6.4 = 262.144 \)
Then \( V=\frac{4}{3}\pi\times262.144 \)
\( V=\frac{1048.576}{3}\pi \)

Step3: Calculate the value of \( V \)

\( V=\frac{1048.576}{3}\times3.14159\) (using \( \pi\approx3.14159 \))
\( V\approx\frac{1048.576\times3.14159}{3}\)
\( 1048.576\times3.14159 = 3294.0117\)
\( V\approx\frac{3294.0117}{3}=1098.0039\)

Answer:

\( 1098.0 \) cubic inches