Question

Is a surface area in square inches of a comb with a radius of 10 inches in a slant height of 15 inches

Answer 1

To calculate the surface area of a comb, we typically consider it as a geometric shape, such as a cone. A comb can be modeled as a cone with a certain height, radius, and slant height.

Given:
- Radius (r) = 10 inches
- Slant height (l) = 15 inches

The surface area \( A \) of a cone (excluding the base area) is given by the formula:

\[
A = \pi r l
\]

Where:
- \( r \) is the radius
- \( l \) is the slant height

Now, substituting the values:

\[
A = \pi \times 10 \, \text{inches} \times 15 \, \text{inches}
\]

Calculating it:

\[
A = 150\pi \, \text{square inches}
\]

Using \( \pi \approx 3.14 \):

\[
A \approx 150 \times 3.14 \approx 471 \, \text{square inches}
\]

So, the surface area of the comb (considered as the lateral surface area of the cone) is approximately \( 471 \) square inches.