Find the volume of a sphere with a radius of 1.8 yards. Leave your answer in terms of pi. Round your answer to the nearest hundredth, if necessary.(1 point)

Responses

7.78π yds3
7.78
𝜋

yds
3
7.78 pi yds cubed

24.43π yds3
24.43
𝜋

yds
3
24.43 pi yds cubed

23.34π yds3
23.34
𝜋

yds
3
23.34 pi yds cubed

7.2π yds3

1 answer

To find the volume \( V \) of a sphere with radius \( r \), we use the formula:

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

For a radius \( r = 1.8 \) yards, we can substitute this value into the formula:

\[ V = \frac{4}{3} \pi (1.8)^3 \]

First, calculate \( (1.8)^3 \):

\[ (1.8)^3 = 1.8 \times 1.8 \times 1.8 = 5.832 \]

Now substitute back into the volume formula:

\[ V = \frac{4}{3} \pi (5.832) \]

Now calculate \( \frac{4}{3} \times 5.832 \):

\[ \frac{4}{3} \times 5.832 \approx 7.776 \]

Thus, the volume in terms of \(\pi\) is:

\[ V \approx 7.776 \pi \text{ yds}^3 \]

Rounding this to the nearest hundredth, we have:

\[ V \approx 7.78 \pi \text{ yds}^3 \]

So the correct response is:

7.78π yds³