Question

Surface Area of Cones Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.

A cone shows a base diameter of 25 centimeters, perpendicular height from the base to the top vertex at 90 degrees, and 22 centimeters as the hypotenuse or the side of the cone.

What is the surface area of the cone? Use 3.14 for pi.

(1 point)
Responses

2,383.26 square centimeters
2,383.26 square centimeters

3,689.5 square centimeters
3,689.5 square centimeters

863.5 square centimeters
863.5 square centimeters

1,354.125 square centimeters
1,354.125 square centimeters
Skip to navigation

Answer 1

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

The base of the cone is a circle, so the area of the base is given by: A = πr^2, where r is the radius of the base.

Given that the diameter of the base is 25 centimeters, the radius is half of that: r = 25/2 = 12.5 centimeters.

Therefore, the area of the base is: A = 3.14 * (12.5)^2 = 3.14 * 156.25 = 490.625 square centimeters.

The curved surface of the cone is a sector of a circle, so its area is given by: A = πrl, where r is the radius of the base, and l is the slant height.

Given that the slant height is 22 centimeters, the area of the curved surface is: A = 3.14 * 12.5 * 22 = 868.5 square centimeters.

Therefore, the total surface area of the cone is the sum of the base area and the curved surface area: 490.625 + 868.5 = 1359.125 square centimeters.

The correct answer is 1,359.125 square centimeters.