Question

A circular cone has a diameter of 8 in. and a slant height of 10 in. What is the surface area of the cone to the nearest inch?
(1 point)
O 63 in.?
• 452 in.?
• 176 in.?
302 in.?

Answer 1

To find the surface area of a cone, you can use the formula:

\[
\text{Surface Area} = \pi r^2 + \pi r l
\]

where \( r \) is the radius of the base, and \( l \) is the slant height.

1. **Find the radius \( r \)**:
- The diameter of the cone is 8 in., so the radius is:
\[
r = \frac{8}{2} = 4 \text{ in.}
\]

2. **Use the given slant height \( l \)**:
- The slant height \( l \) is given as 10 in.

3. **Calculate the surface area**:
- Substitute \( r \) and \( l \) into the surface area formula:
\[
\text{Surface Area} = \pi (4^2) + \pi (4)(10)
\]
\[
= \pi (16) + \pi (40)
\]
\[
= 16\pi + 40\pi
\]
\[
= 56\pi
\]

4. **Calculate \( 56\pi \)** using \( \pi \approx 3.14 \):
\[
56\pi \approx 56 \times 3.14 = 175.84 \text{ in}^2
\]

5. **Round to the nearest inch**:
\[
\approx 176 \text{ in}^2
\]

Therefore, the surface area of the cone is approximately **176 in²**.

The correct answer is **176 in²**.