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 calculate the area of the base and the lateral area.
1. The area of the base is given by the formula: A_base = π * r^2, where r is the radius of the base. Since the diameter is 25 cm, the radius is half of that, so r = 25/2 = 12.5 cm. Therefore, A_base = 3.14 * (12.5)^2 = 3.14 * 156.25 = 490.625 cm^2.
2. The lateral area of the cone is given by the formula: A_lateral = π * r * l, where l is the slant height. We can use the Pythagorean theorem to find l. We have the height and the hypotenuse, so we can calculate l = sqrt(h^2 + r^2) = sqrt(22^2 + 12.5^2) = sqrt(484 + 156.25) = sqrt(640.25) = 25.3 cm. Therefore, A_lateral = 3.14 * 12.5 * 25.3 = 998.08 cm^2.
Now, we can find the total surface area by adding the base area and the lateral area: S = A_base + A_lateral = 490.625 + 998.08 = 1488.705 cm^2.
Therefore, the surface area of the cone is approximately 1488.705 cm^2.
Wrong.
Apologies for the mistake.
To find the surface area of a cone, we need to calculate the area of the base and the lateral area.
1. The area of the base is given by the formula A_base = π * r^2, where r is the radius of the base. Since the diameter is 25 cm, the radius is half of that, so r = 25/2 = 12.5 cm. Therefore, A_base = 3.14 * (12.5)^2 = 3.14 * 156.25 = 490.625 cm^2.
2. The lateral area of the cone is given by the formula A_lateral = π * r * l, where l is the slant height. We can use the Pythagorean theorem to find l. We have the height and the hypotenuse, so we can calculate l = sqrt(h^2 + r^2) = sqrt(22^2 + 12.5^2) = sqrt(484 + 156.25) = sqrt(640.25) = 25.3 cm.
Therefore, the lateral area A_lateral = 3.14 * 12.5 * 25.3 = 1,000.825 cm^2.
Now, we can find the total surface area by adding the base area and the lateral area: S = A_base + A_lateral = 490.625 + 1,000.825 = 1,491.45 cm^2.
Therefore, the surface area of the cone is approximately 1,491.45 cm^2.