Use the formula for the volume of a sphere to solve the following problem. How much air is needed to fill a basketball with a diameter of 9 inches? Use 3.14 as an approximation for pi. Round your answer to the nearest tenth. (1 point) Responses 3,052.1 in.3 3,052.1 inches cubed 113 in.3 113 inches cubed 190.8 in.3 190.8 inches cubed 381.5 in.3
The formula for the volume of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume, and \( r \) is the radius of the sphere.
Given that the diameter of the basketball is 9 inches, the radius \( r \) will be half of that:
\[ r = \frac{diameter}{2} = \frac{9\ inches}{2} = 4.5\ inches \]
Now we can use the formula to calculate the volume, using 3.14 as an approximation for pi:
\[ V = \frac{4}{3} \cdot 3.14 \cdot (4.5\ inches)^3 \]
\[ V = \frac{4}{3} \cdot 3.14 \cdot 91.125\ in^3 \]
\[ V = 4.18667 \cdot 91.125\ in^3 \]
\[ V = 381.50625\ in^3 \]
Rounded to the nearest tenth, the volume of the basketball would be:
\[ V \approx 381.5\ in^3 \]
Thus, the correct option is \( 381.5\ inches \) cubed.