Question

Judy has a sugar cone and wants to know how many cubic inches of ice cream it will hold if it is filled completely to the top of the cone and no more. The cone has a height of 4.5 inches and a radius of 1.5 inches.
Responses
A 7.1 cubic inches7.1 cubic inches
B 10.6 cubic inches10.6 cubic inches
C 14.1 cubic inches14.1 cubic inches
D 31.8 cubic inches

Answer 1

To calculate 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 of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is approximately \( 3.14 \).

Given:
- \( r = 1.5 \) inches,
- \( h = 4.5 \) inches.

First, calculate the area of the base of the cone:

\[
r^2 = (1.5)^2 = 2.25
\]

Now plug the values into the volume formula:

\[
V = \frac{1}{3} \pi (2.25)(4.5)
\]

Calculating \( 2.25 \times 4.5 \):

\[
2.25 \times 4.5 = 10.125
\]

Now substitute this back into the volume formula:

\[
V = \frac{1}{3} \pi (10.125)
\]

Now approximate using \( \pi \approx 3.14 \):

\[
V \approx \frac{1}{3} \times 3.14 \times 10.125
\]

Calculating \( 3.14 \times 10.125 \):

\[
3.14 \times 10.125 \approx 31.71
\]

Now divide this by 3:

\[
V \approx \frac{31.71}{3} \approx 10.57
\]

Thus, the volume is approximately \( 10.57 \) cubic inches.

Among the given choices, the closest option is:

**B: 10.6 cubic inches**.