Question

A spyglass in the shade of a cone has a slant height if 18 centimeters and a radius of 6 centimeters what is the surface are of the spyglass use 3.14 for pi

Answer 1

To find the surface area of the spyglass, we need to find the curved surface area of the cone and add the base area.

The curved surface area of a cone is given by the formula:
CSA = πrℓ, where r is the radius and ℓ is the slant height.

Given that the radius (r) of the spyglass is 6 centimeters and the slant height (ℓ) is 18 centimeters, we can calculate the curved surface area:
CSA = 3.14 * 6 * 18
CSA = 339.12 square centimeters (rounded to two decimal places)

The base area of a cone is given by the formula:
Base Area = πr^2

Given that the radius (r) of the spyglass is 6 centimeters, we can calculate the base area:
Base Area = 3.14 * 6^2
Base Area = 113.04 square centimeters

To find the total surface area, we add the curved surface area to the base area:
Total Surface Area = CSA + Base Area
Total Surface Area = 339.12 + 113.04
Total Surface Area = 452.16 square centimeters (rounded to two decimal places)

The surface area of the spyglass is 452.16 square centimeters.