Use the formula for the volume of a sphere to find the volume of a basketball that has a diameter of 9.2 inches. Use 3.14 as an approximation for pi and round your answer to the nearest hundredth, if necessary.(1 point)

Question

Responses

115.55 in.3
115.55 inches cubed

407.51 in.3
407.51 inches cubed

3,260.11 in.3
3,260.11 inches cubed

1,222.54 in.3

Answer 1

To find the volume of a sphere, you can use the formula:

\[ V = \frac{4}{3}\pi r^3 \]

where \( V \) is the volume, \( \pi \) is Pi (approximately 3.14), and \( r \) is the radius of the sphere. The radius is half the diameter, so for a basketball with a diameter of 9.2 inches, the radius \( r \) is:

\[ r = \frac{9.2 \text{ inches}}{2} = 4.6 \text{ inches} \]

Now plug the radius into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times (4.6)^3 \]

Calculate the volume:

\[ V = \frac{4}{3} \times 3.14 \times 4.6^3 \]
\[ V = \frac{4}{3} \times 3.14 \times 97.336 \]
\[ V = 4.18667 \times 97.336 \]
\[ V \approx 407.72 \]

Rounded to the nearest hundredth:

\[ V \approx 407.72 \, \text{in}^3 \]

So, the closest answer is:

407.51 inches cubed