Question

Note: Figure is not drawn to scale.

If h = 24 units and r = 8 units, what is the volume of the cone shown above?
Use 3.14 for .
A.
1,607.68 cubic units
B.
200.96 cubic units
C.
4,823.04 cubic units
D.
602.88 cubic units

Answer 1

The volume \( V \) of a cone can be calculated using the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

Given:
- \( h = 24 \) units
- \( r = 8 \) units
- \( \pi \approx 3.14 \)

Now, substitute the values into the formula:

\[
V = \frac{1}{3} \times 3.14 \times (8)^2 \times 24
\]

First, calculate \( (8)^2 \):

\[
(8)^2 = 64
\]

Now, plug this value into the equation:

\[
V = \frac{1}{3} \times 3.14 \times 64 \times 24
\]

Next, calculate \( 64 \times 24 \):

\[
64 \times 24 = 1536
\]

Now substitute this into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 1536
\]

Now, calculate \( 3.14 \times 1536 \):

\[
3.14 \times 1536 = 4825.44
\]

Finally, divide by 3:

\[
V = \frac{4825.44}{3} \approx 1608.48
\]

Therefore, rounding to two decimal places, the volume \( V \) is approximately \( 1,608.48 \).

However, since we have to choose from the options given, the closest answer is:

**A. 1,607.68 cubic units**.