The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere. We are given that the volume of the sphere is 800 cubic inches. We can set up the equation:
\[ \frac{4}{3} \pi r^3 = 800 \]
To solve for \( r \), first multiply both sides by \( \frac{3}{4} \):
\[ \pi r^3 = \frac{3 \times 800}{4} \]
\[ \pi r^3 = 600 \]
Next, divide both sides by \( \pi \):
\[ r^3 = \frac{600}{\pi} \]
Now, we can use the approximate value of \( \pi \approx 3.14 \):
\[ r^3 \approx \frac{600}{3.14} \approx 191.08 \]
To find \( r \), we take the cube root:
\[ r \approx \sqrt[3]{191.08} \]
Calculating the cube root:
\[ r \approx 5.76 \]
Therefore, the approximate value of \( r \), the radius of the sphere, is:
A. 5.76