Question

find the volume of a sphere with a radius of 9. 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 \( r = 9 \), we substitute \( r = 9 \) into the formula:
\( V=\frac{4}{3}\pi(9)^{3} \)

Step3: Calculate \( 9^{3} \)

First, calculate \( 9^{3}=9\times9\times9 = 729 \). So now the formula becomes \( V=\frac{4}{3}\pi\times729 \).

Step4: Simplify the expression

Calculate \( \frac{4}{3}\times729 \). We know that \( 729\div3 = 243 \), and then \( 243\times4=972 \). So \( V = 972\pi \). If we use the approximation \( \pi\approx3.14159 \), then \( V\approx972\times3.14159 \).

Step5: Compute the numerical value

\( 972\times3.14159 = 972\times3+972\times0.14159=2916 + 137.62548=3053.62548 \). Rounding to the nearest hundredth, we get \( 3053.63 \) (if we consider the decimal approximation) or we can leave it in terms of \( \pi \) as \( 972\pi\approx3053.63 \).

Answer:

The volume of the sphere is \( 972\pi\) (or approximately \( 3053.63 \))