Question

Find the volume of a sphere with a radius of 1.8 yards. Leave your answer in terms of pi. Round to the nearest hundredth

Answer 1

To find the volume of a sphere, you can use the formula:

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

where \( V \) is the volume and \( r \) is the radius of the sphere.

Given that the radius \( r = 1.8 \) 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 substitute \( 1.8^3 \) back into the volume formula:

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

Now calculate \( \frac{4}{3} \times 5.832 \):

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

Thus, the volume in terms of \(\pi\) is:

\[
V = 7.776 \pi
\]

To find the numerical value, multiply \( 7.776 \) by \( \pi \):

Using \( \pi \approx 3.14159 \):

\[
V \approx 7.776 \times 3.14159 \approx 24.436
\]

Rounding to the nearest hundredth, the volume of the sphere is approximately:

\[
\boxed{24.44} \text{ cubic yards}
\]

In terms of \(\pi\), the volume is:

\[
\boxed{7.776\pi} \text{ cubic yards}
\]