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. For a sphere with a radius of 1.8 yards, we can substitute \( r = 1.8 \) 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 value back into the volume formula:
\[ V = \frac{4}{3} \pi (5.832) \]
Calculating \( \frac{4}{3} \times 5.832 \):
\[ \frac{4 \times 5.832}{3} = \frac{23.328}{3} \approx 7.776 \]
Thus, the volume in terms of \( \pi \) is:
\[ V \approx 7.776 \pi \]
Now rounding \( 7.776 \) to the nearest hundredth:
\[ V \approx 7.78 \pi \]
Therefore, the final answer for the volume of the sphere in terms of \( \pi \) is:
\[ V \approx 7.78 \pi \text{ cubic yards} \]
3 answers