To find the volume of a sphere, you use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere. For a sphere with a radius of 1.8 yards, the calculation would be:
\[ V = \frac{4}{3} \pi (1.8)^3 \]
First, calculate \( (1.8)^3 \):
\[ (1.8)^3 = 1.8 \times 1.8 \times 1.8 = 5.832 \]
Then plug this value 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:
\[ V \approx 7.776 \pi \text{ yds}^3 \]
Rounding \( 7.776 \) to the nearest hundredth gives you \( 7.78 \).
Thus, the volume of the sphere is:
\[ 7.78 \pi \text{ yds}^3 \]
From the options provided, the correct answer is:
7.78π yds³