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)

O 24.43T yds3
O 7.21 yds3
• 23.34T yds3
O 7.78T yds3

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.

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 back into the volume formula:

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

Calculate \( \frac{4}{3} \times 5.832 \):

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

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

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

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

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

So the answer is:

7.78T yds³.