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) 339.12 square centimeters 197.82 square centimeters 452.16 square centimeters 1,356.48 square centimeters

Explanation:

Step1: Calculate the lateral surface area

The formula for the lateral surface area of a cone is \( \pi rl\), where \(r\) is the radius and \(l\) is the slant height.
Substitute \(r = 6\) and \(l=18\) and \(\pi = 3.14\)
\(3.14\times6\times18=339.12\)

Step2: Calculate the base area

The formula for the area of a circle (base of the cone) is \(\pi r^{2}\)
Substitute \(r = 6\) and \(\pi=3.14\)
\(3.14\times6^{2}=3.14\times36 = 113.04\)

Step3: Calculate the total surface area

The total surface area of a cone \(A=\pi rl+\pi r^{2}\)
\(A=339.12 + 113.04=452.16\)

Answer:

452.16 square centimeters