What is the surface area of the cone? Use 3.14 for pi. diameter =25 cm 22cm for sides (1 point) Responses 2,383.26 square centimeters 2,383.26 square centimeters 1,354.125 square centimeters 1,354.125 square centimeters 3,689.5 square centimeters 3,689.5 square centimeters 863.5 square centimeters
The surface area of a cone consists of two parts: the base area and the lateral surface area.
The base of the cone is a circle with the diameter given as 25 cm. The radius r of the base is half the diameter, so r = 25 cm / 2 = 12.5 cm.
The base area can be calculated using the formula for the area of a circle: A = πr², where π (pi) is approximately 3.14.
The base area is then: A_base = π * (12.5 cm)² = 3.14 * 156.25 cm² = 490.625 cm².
Next, we need to calculate the lateral surface area of the cone, which can be found using the formula: A_lateral = πrl, where r is the radius of the base and l is the slant height (also referred to as the "side" in the question).
Given that the side/slant height l is 22 cm, the lateral surface area is: A_lateral = π * 12.5 cm * 22 cm = 3.14 * 12.5 cm * 22 cm = 3.14 * 275 cm² = 863.5 cm².
Adding the base area and the lateral surface area together gives the total surface area of the cone.
Total surface area = A_base + A_lateral = 490.625 cm² + 863.5 cm² = 1354.125 cm².
Therefore, the surface area of the cone is 1,354.125 square centimeters.