Question

what is the volume of a sphere with a radius of 41 in, rounded to the nearest tenth of a cubic inch?

Explanation:

Step1: Recall 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 given radius into the formula

Given that the radius \( r = 41 \) inches. Substitute \( r = 41 \) into the formula:
\( V=\frac{4}{3}\pi(41)^{3} \)
First, calculate \( 41^{3}=41\times41\times41 = 41\times1681=68921 \)
Then, \( V=\frac{4}{3}\pi\times68921=\frac{275684}{3}\pi \)

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have:
\( V=\frac{275684}{3}\times3.14159\approx91894.6667\times3.14159\approx288695.9 \) (rounded to the nearest tenth)

Answer:

The volume of the sphere is approximately \( 288695.9 \) cubic inches.