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

1 answer

The formula for the volume \( V \) of a sphere is given by:

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

where \( r \) is the radius of the sphere.

Given the radius \( r = 1.8 \) yards, we can substitute this value into the formula:

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

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

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

Now we substitute this value back into the formula for the volume:

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

Next, we multiply \( \frac{4}{3} \) by \( 5.832 \):

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

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

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

Rounding \( 7.776 \) to the nearest hundredth gives us \( 7.78 \).

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

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

Among the options given, the correct response is:

7.78π yds³