Question

A)A highway traffic cone consists of a cone centered on a square prism base. The cone has a height of 36 in. and a diameter of 10 in. The sides of the base are 14.5 in., and the height is 1.5 in. If the traffic cone was solid, what would be its volume? Round your answer to the nearest whole number.(1 point)
Responses

1,258 in.3
1,258 inches cubed

942 in.3
942 inches cubed

615 in.3
615 inches cubed

3,143 in.3

Answer 1

To find the volume of the solid traffic cone, we first calculate the volume of the cone and then we can verify if any other components (such as the square prism) need to be included.

### Volume of the Cone

The formula for the volume of a cone is given by:

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

where:
- \( r \) is the radius,
- \( h \) is the height.

1. **Find the radius**:
The diameter of the cone is 10 inches, so the radius \( r \) is:
\[
r = \frac{10}{2} = 5 \text{ inches}
\]

2. **Height of the cone**:
The height \( h \) is given as 36 inches.

3. **Plug values into the volume formula**:
\[
V = \frac{1}{3} \pi (5)^2 (36)
\]
\[
V = \frac{1}{3} \pi (25)(36)
\]
\[
V = \frac{1}{3} \pi (900)
\]
\[
V = 300\pi
\]

4. **Calculate using \( \pi \approx 3.14159 \)**:
\[
V \approx 300 \times 3.14159 \approx 942.477
\]

Rounding to the nearest whole number gives:

\[
V \approx 942 \text{ in}^3
\]

### Conclusion
The volume of the solid traffic cone is approximately **942 inches cubed**.

So, the correct answer from the responses is \( \text{942 in}^3 \) or \( 942 \text{ inches cubed} \).