Question

The diameter of a large lawn ornament in the shape of a sphere is 16 inches. What is the approximate volume of the ornament? Use 3.14 for Pi. Round to the nearest tenth of a cubic inch.

Recall the formula V = four-thirds pi r cubed.

Answer 1

To find the volume of the sphere-shaped lawn ornament, we start with the formula for the volume of a sphere:

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

First, we need to determine the radius \( r \). Since the diameter of the sphere is given as 16 inches, we can calculate the radius as follows:

\[
r = \frac{\text{diameter}}{2} = \frac{16 \text{ inches}}{2} = 8 \text{ inches}
\]

Next, we can substitute the radius and the value of \(\pi\) into the volume formula. Using \(\pi = 3.14\):

\[
V = \frac{4}{3} \times 3.14 \times (8)^3
\]

Now we calculate \( (8)^3 \):

\[
(8)^3 = 512
\]

Substituting this value back into the equation:

\[
V = \frac{4}{3} \times 3.14 \times 512
\]

Now calculate \( \frac{4}{3} \times 512 \):

\[
\frac{4}{3} \times 512 = \frac{2048}{3} \approx 682.6667
\]

Now, multiply this by \( 3.14 \):

\[
V \approx 682.6667 \times 3.14 \approx 2146.7333
\]

Finally, rounding to the nearest tenth:

\[
V \approx 2146.7
\]

Thus, the approximate volume of the ornament is

\[
\boxed{2146.7} \text{ cubic inches}.
\]