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 24.43π yds3 24.43 pi yds cubed 23.34π yds3 23.34 pi yds cubed 7.78π yds3 7.78 pi yds cubed 7.2π 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 \( r = 1.8 \) 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 this value back into the volume formula:

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

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

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

So the volume in terms of \( \pi \) is:

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

Now rounding \( 7.776 \) to the nearest hundredth gives:

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

Based on the options provided, the correct response is:

7.78π yds³