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. 23.34π yds3
2. 7.78π yds3
3. 24.43π yds3
4. 7.2π yds3

1 answer

The volume \( V \) of a sphere can be calculated using 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 substitute this value into the formula:

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

Now, we need to calculate \( (1.8)^3 \):

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

Now, substituting this back into the volume formula:

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

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

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

Thus, we can express the volume as:

\[ V \approx 7.776\pi \]

Now, rounding this to the nearest hundredth, we get:

\[ V \approx 7.78\pi \]

Therefore, the answer in terms of \(\pi\) is:

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

Among the choices provided, the correct answer is:

2. 7.78π yds³