Question

find the volume of a sphere with a radius of 7. round your answer to the nearest hundredth if necessary. show your work here hint: to add the pi symbol (π), type \pi\

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 \( r = 7 \). Substitute \( r = 7 \) into the formula:
\( V=\frac{4}{3}\pi(7)^{3} \)
First, calculate \( 7^{3}=7\times7\times7 = 343 \)
So, \( V=\frac{4}{3}\pi\times343=\frac{1372}{3}\pi\approx\frac{1372}{3}\times3.14159265 \)

Step3: Calculate the numerical value

\( \frac{1372}{3}\times3.14159265\approx457.333\cdots\times3.14159265\approx1436.755 \) (rounded to the nearest hundredth)

Answer:

The volume of the sphere is approximately \( 1436.76 \) (if we use \( \pi\approx3.1416 \)) or \( \frac{1372}{3}\pi\approx1436.76 \)