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
1,354.125 square centimeters
1,354.125 square centimeters
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
To find the surface area of the cone, we need to calculate both the base area and the lateral (side) surface area.
First, let's find the base area, which is the area of the circle:
The base radius (r) is half of the diameter, so r = 25 cm / 2 = 12.5 cm.
The base area (A_base) = π * r^2 = 3.14 * (12.5 cm)^2 = 3.14 * 156.25 cm^2 = 490.625 cm^2.
Next, we need to find the lateral surface area (A_lateral) of the cone. The lateral surface area of a cone is given by the formula:
A_lateral = π * r * l,
where l is the slant height of the cone, which in this case is 22 cm.
A_lateral = 3.14 * 12.5 cm * 22 cm = 3.14 * 275 cm^2 = 863.5 cm^2.
Now, we sum up the base area and the lateral surface area to get the total surface area of the cone:
Total surface area (A_total) = A_base + A_lateral = 490.625 cm^2 + 863.5 cm^2 = 1,354.125 cm^2.
Hence, the surface area of the cone is 1,354.125 square centimeters. The correct response is:
1,354.125 square centimeters.