To find the volume of a basketball (which is a sphere) using the formula for the volume of a sphere, use the following formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume, \( \pi \) is approximately 3.14, and \( r \) is the radius of the sphere.
- First, find the radius. The diameter of the basketball is 9.2 inches, so the radius \( r \) is half of that:
\[ r = \frac{9.2}{2} = 4.6 , \text{inches} \]
- Now, substitute the radius into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (4.6)^3 \]
- Calculate \( (4.6)^3 \):
\[ (4.6)^3 = 4.6 \times 4.6 \times 4.6 \approx 97.336 \]
- Now substitute this value back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 97.336 \]
- Calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
- Now multiply this by \( 97.336 \):
\[ V \approx 4.18667 \times 97.336 \approx 407.135 \]
- Finally, round to the nearest hundredth:
\[ V \approx 407.14 , \text{in}^3 \]
From the options provided, the closest one is:
407.51 in.³.
1 answer