Question

A spyglass in the shape of a cone has a slant height of 18 centimeters and a radius of 6 centimeters. What is the surface area of the spyglass? Use 3.14 for pi.(1 point) Responses 452.16 square centimeters 452.16 square centimeters 339.12 square centimeters 339.12 square centimeters 1,356.48 square centimeters 1,356.48 square centimeters 197.82 square centimeters

Answer 1

To find the surface area of the cone-shaped spyglass, we need to calculate both the lateral surface area and the base area of the cone.

1. **Lateral Surface Area (LSA)**:
The formula for the lateral surface area of a cone is given by:
\[
LSA = \pi r l
\]
where \( r \) is the radius and \( l \) is the slant height.

Here, \( r = 6 \) cm and \( l = 18 \) cm. Thus:
\[
LSA = 3.14 \times 6 \times 18
\]
\[
LSA = 3.14 \times 108 = 339.12 \text{ square centimeters}
\]

2. **Base Area (BA)**:
The formula for the area of the base (which is a circle) is given by:
\[
BA = \pi r^2
\]
Using \( r = 6 \) cm:
\[
BA = 3.14 \times 6^2 = 3.14 \times 36 = 113.04 \text{ square centimeters}
\]

3. **Total Surface Area (TSA)**:
The total surface area of the cone is given by:
\[
TSA = LSA + BA
\]
Substituting the values we calculated:
\[
TSA = 339.12 + 113.04 = 452.16 \text{ square centimeters}
\]

Thus, the surface area of the spyglass is **452.16 square centimeters**.