To solve for the radius [tex]\( r \)[/tex] of a sphere when given its volume [tex]\( V \)[/tex], we start with the volume formula for a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Given the volume [tex]\( V = 288 \)[/tex] cubic inches, and using [tex]\( \pi \approx 3.14 \)[/tex], we substitute these values into the equation:
[tex]\[ 288 = \frac{4}{3} \times 3.14 \times r^3 \][/tex]
First, simplify the constants on the right-hand side:
[tex]\[ \frac{4}{3} \times 3.14 = 4.1866667 \][/tex]
So the equation simplifies to:
[tex]\[ 288 = 4.1866667 \times r^3 \][/tex]
Next, solve for [tex]\( r^3 \)[/tex] by isolating it:
[tex]\[ r^3 = \frac{288}{4.1866667} \][/tex]
By performing the division:
[tex]\[ r^3 \approx 68.7898 \][/tex]
Now, to find the radius [tex]\( r \)[/tex], take the cube root of both sides of the equation:
[tex]\[ r = \sqrt[3]{68.7898} \][/tex]
Performing the cube root calculation gives:
[tex]\[ r \approx 4.0974 \][/tex]
Finally, round this value to the nearest tenth of an inch:
[tex]\[ r \approx 4.1 \][/tex]
So, the radius of the volleyball, to the nearest tenth of an inch, is:
[tex]\[ \boxed{4.1} \][/tex]
The correct answer is B. 4.1 inches.
