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) Responses 3,260.11 in.3 3,260.11 inches cubed 407.51 in.3 407.51 inches cubed 1,222.54 in.3 1,222.54 in cubed 115.55 in.3
To find the volume of a sphere, we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Where:
- \( V \) is the volume of the sphere
- \( \pi \) is a constant (use 3.14 for pi as instructed)
- \( r \) is the radius of the sphere
Since the diameter of the basketball is given as 9.2 inches, we first need to find the radius. The radius is half the diameter, thus:
\[ r = \frac{diameter}{2} = \frac{9.2}{2} = 4.6 \text{ inches} \]
Now we can plug the radius into the volume formula to find the volume of the basketball:
\[ V = \frac{4}{3} \cdot 3.14 \cdot (4.6)^3 \]
\[ V = \frac{4}{3} \cdot 3.14 \cdot 97.336 \]
\[ V = 4.188 \cdot 97.336 \]
\[ V = 407.752896 \text{ cubic inches} \]
Rounded to the nearest hundredth, this becomes:
\[ V \approx 407.75 \text{ in}^3 \]
So the volume of the basketball is approximately 407.75 cubic inches.