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)

Question

23.34 pi yds³

24.43 pi yds³

7.78 pi yds³

7.2 pi yds³

Answer 1

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:

1. Calculate \( r^3 \): \[ r^3 = (1.8)^3 = 1.8 \times 1.8 \times 1.8 = 5.832 \]

2. Now, substitute \( r^3 \) into the volume formula: \[ V = \frac{4}{3} \pi (5.832) = \frac{4 \times 5.832}{3} \pi = \frac{23.328}{3} \pi \approx 7.776 \pi \]

3. Therefore, the volume of the sphere in terms of \( \pi \) is: \[ V \approx 7.78 \pi \text{ yds}^3 \]

The answer rounded to the nearest hundredth is:

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