Question

find the volume of a sphere with a radius of 5. 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 with radius \( r \) is \( V=\frac{4}{3}\pi r^{3} \).

Step2: Substitute the given radius into the formula

Given that the radius \( r = 5 \), we substitute \( r = 5 \) into the formula:
\( V=\frac{4}{3}\pi(5)^{3} \)
First, calculate \( 5^{3}=5\times5\times5 = 125 \).
Then, \( V=\frac{4}{3}\pi\times125=\frac{500}{3}\pi\approx\frac{500}{3}\times3.14159265\)
\( \frac{500\times3.14159265}{3}=\frac{1570.796325}{3}\approx523.598775 \)

Step3: Round to the nearest hundredth

Rounding \( 523.598775 \) to the nearest hundredth gives \( 523.60 \) (since the thousandth digit is 8, which is greater than or equal to 5, we round up the hundredth digit 9 to 10, carrying over to the tenths place: the tenths digit 5 becomes 6 and the hundredth digit becomes 0).

Answer:

The volume of the sphere is approximately \( 523.60 \) (or \( \frac{500}{3}\pi\approx523.60 \)).