Question

Sid is packing crushed ice into a cone-shaped cup. The cone has a height of 5 in. Its base has a diameter of 4 in. What is the volume of the cone?
StartFraction 20 Over 3 EndFraction pi inches cubed
20 pi inches cubed
StartFraction 80 Over 3 EndFraction pi inches cubed
80 pi inches cubed

Answer 1

To find the volume of a cone, we use the formula:

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

Where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height.

Given:
- The height \( h = 5 \) inches,
- The diameter of the base is 4 inches, so the radius \( r = \frac{4}{2} = 2 \) inches.

Now we can substitute these values into the volume formula:

\[
V = \frac{1}{3} \pi (2^2) (5)
\]

Calculating \( r^2 \):

\[
r^2 = 2^2 = 4
\]

Now substitute \( r^2 \) into the volume formula:

\[
V = \frac{1}{3} \pi (4) (5)
\]

Multiply \( 4 \) and \( 5 \):

\[
V = \frac{1}{3} \pi (20)
\]

Now simplify this:

\[
V = \frac{20}{3} \pi
\]

Thus, the volume of the cone is

\[
\frac{20}{3} \pi \text{ inches}^3.
\]

The correct answer is:

\[
\frac{20}{3} \pi \text{ inches}^3.
\]