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
863.5 square centimeters
863.5 square centimeters
3,689.5 square centimeters
3,689.5 square centimeters
2,383.26 square centimeters
2,383.26 square centimeters
1,354.125 square centimeters
To find the surface area of a cone, you need to calculate the lateral surface area, which is the curved surface area of the cone, and add it to the base area.
The lateral surface area of a cone is given by the formula:
Lateral Surface Area = π × radius × slant height
Since the radius is half of the base diameter, which is 25 cm / 2 = 12.5 cm,
And the slant height is given as 22 cm,
Lateral Surface Area = 3.14 × 12.5 cm × 22 cm
Lateral Surface Area = 3.14 × 275 cm²
Lateral Surface Area = 863.5 cm²
The base area of a cone is given by the formula:
Base Area = π × radius²
Base Area = 3.14 × (12.5 cm)²
Base Area = 3.14 × 156.25 cm²
Base Area = 490.625 cm²
To find the surface area, we add the lateral surface area and the base area:
Surface Area = Lateral Surface Area + Base Area
Surface Area = 863.5 cm² + 490.625 cm²
Surface Area = 1354.125 cm²
So, the surface area of the cone is 1354.125 square centimeters.