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

1,222.54 in.3
1
,
222.54

in.
3
1,222.54 in cubed

407.51 in.3
407.51

in.
3
407.51 inches cubed

3,260.11 in.3
3
,
260.11

in
.
3
3,260.11 inches cubed

115.55 in.3

1 answer

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

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

where \( V \) is the volume and \( r \) is the radius of the sphere.

First, we need to find the radius from the diameter. The diameter of the basketball is 9.2 inches, so the radius \( r \) is:

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

Next, we can substitute the radius into the volume formula, using \( \pi \approx 3.14 \):

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

Calculating \( (4.6)^3 \):

\[ (4.6)^3 = 4.6 \times 4.6 \times 4.6 = 97.336 \text{ in}^3 \]

Now substituting into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times 97.336 \]

Calculating \( \frac{4}{3} \times 3.14 \):

\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]

Now, multiplying this by \( 97.336 \):

\[ V \approx 4.18667 \times 97.336 \approx 407.51 \text{ in}^3 \]

So the volume of the basketball is approximately 407.51 in³ when rounded to the nearest hundredth.

Thus, the correct response is:

407.51 in.³