Question

find the volume of a sphere with a radius of 8. 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

We are given that the radius \( r = 8 \). Substituting \( r = 8 \) into the formula, we get \( V=\frac{4}{3}\pi(8)^{3} \).

Step3: Calculate \( 8^{3} \)

First, calculate \( 8^{3}=8\times8\times8 = 512 \). So now the formula becomes \( V=\frac{4}{3}\pi\times512 \).

Step4: Multiply \( \frac{4}{3} \) and \( 512 \)

\( \frac{4}{3}\times512=\frac{2048}{3} \). So the volume is \( V = \frac{2048}{3}\pi \). If we want to use the approximate value of \( \pi\approx3.14159 \), then \( V=\frac{2048}{3}\times3.14159 \).

Step5: Calculate the numerical value

\( \frac{2048}{3}\times3.14159\approx682.6667\times3.14159\approx2144.66 \) (rounded to the nearest hundredth).

Answer:

If we use the exact form with \( \pi \), the volume is \( \frac{2048}{3}\pi \approx 2144.66 \) (rounded to the nearest hundredth).