To find the surface area of a cone, we need to calculate the lateral surface area and the base area.
The lateral surface area can be calculated using the formula:
lateral surface area = pi × r × l
where r is the radius of the base and l is the slant height of the cone.
Given that the base diameter is 25 centimeters, the radius (r) is half of that, which is 12.5 centimeters. The hypotenuse is given as 22 centimeters, which is the slant height (l).
Substituting these values into the formula, we get:
lateral surface area = 3.14 × 12.5 × 22 ≈ 863.5 square centimeters
Next, we need to calculate the base area. The base of the cone is a circle, and its area can be calculated using the formula:
base area = pi × r^2
Substituting the radius (r) of 12.5 centimeters into the formula, we get:
base area = 3.14 × 12.5^2 = 3.14 × 156.25 ≈ 490.875 square centimeters
Adding the lateral surface area and the base area, we get:
surface area = lateral surface area + base area
surface area = 863.5 + 490.875 ≈ 1354.375 square centimeters
Therefore, the closest answer is:
1,354.125 square centimeters
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
1,354.125 square centimeters
1,354.125 square centimeters
3,689.5 square centimeters
3,689.5 square centimeters
2,383.26 square centimeters
1 answer