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.