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.
To find the surface area of a cone, we need to find the lateral surface area and the base area.
The lateral surface area of a cone can be found using the formula:
Lateral surface area = π × base diameter × slant height
Here, the base diameter is 25 centimeters and the slant height is 22 centimeters.
Lateral surface area = 3.14 × 25 × 22
Lateral surface area = 1,725.5 square centimeters (rounded to the nearest tenth)
The base area of a cone can be found using the formula:
Base area = 0.5 × π × base diameter^2
Here, the base diameter is 25 centimeters.
Base area = 0.5 × 3.14 × 25^2
Base area = 0.5 × 3.14 × 625
Base area = 981.25 square centimeters (rounded to the nearest hundredth)
Therefore, the surface area of the cone is the sum of the lateral surface area and the base area:
Surface area = Lateral surface area + Base area
Surface area = 1,725.5 + 981.25
Surface area = 2,706.75 square centimeters (rounded to the nearest hundredth)
The surface area of the cone is approximately 2,706.75 square centimeters.