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

1 answer

The volume \( V \) of a sphere is calculated using the formula:

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

where \( r \) is the radius of the sphere. Given that the radius \( r = 1.8 \) yards, we can substitute that value into the formula.

First, calculate \( r^3 \):

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

Now use the volume formula:

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

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

\[ 4 \times 5.832 = 23.328 \] \[ \frac{23.328}{3} = 7.776 \]

Now substituting back into the volume formula gives:

\[ V = 7.776 \pi \]

Rounding this to the nearest hundredth, we have:

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

Thus, the correct response is:

7.78π yds³.