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)

7.78π yds3 7.78 pi yds cubed 23.34π yds3 23.34 pi yds cubed 7.2π yds3 7.2 pi yds cubed 24.43π yds3

1 answer

To find the volume \( V \) of a sphere, you can use the formula:

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

where \( r \) is the radius of the sphere.

Given that the radius \( r \) is 1.8 yards, we can calculate the volume as follows:

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

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

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

Now substitute this value back into the volume formula:

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

Next, 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 gives:

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

Therefore, the final answer is:

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