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.

Inches cubed

Answer 1

To find the volume of the lawn ornament, we will use the formula for the volume of a sphere:

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

First, we need to determine the radius \( r \) from the diameter. The radius is half the diameter:

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

Next, we plug in the value of \( r \) and \( \pi \) (using 3.14) into the volume formula:

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

Calculating \( (8)^3 \):

\[
8^3 = 512
\]

Now substituting this value back into the volume formula:

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

Calculating \( \frac{4}{3} \times 512 \):

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

Now, multiplying this by \( \pi \) (3.14):

\[
V \approx 682.6667 \times 3.14 \approx 2146.3333
\]

Rounding this to the nearest tenth:

\[
V \approx 2146.3
\]

Thus, the approximate volume of the ornament is:

\[
\boxed{2146.3} \text{ cubic inches}
\]