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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
3,689.5 square centimeters
3,689.5 square centimeters
863.5 square centimeters
863.5 square centimeters
2,383.26 square centimeters
2,383.26 square centimeters
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To find the surface area of the cone, we need to calculate the lateral surface area and the base area separately.
The lateral surface area of a cone can be found by using the formula:
L = πrℓ
where L is the lateral surface area, π is the approximation for pi (3.14), r is the radius of the base (diameter/2), and ℓ is the slant height (hypotenuse).
Given that the base diameter is 25 centimeters, the radius would be 25/2 = 12.5 centimeters. The slant height is given as 22 centimeters.
L = 3.14 * 12.5 * 22
L ≈ 863.5 square centimeters
The base area of a cone can be found by using the formula:
B = πr^2
where B is the base area and r is the radius of the base.
Given that the radius is 12.5 centimeters,
B = 3.14 * (12.5)^2
B ≈ 490.875 square centimeters
The total surface area of the cone is the sum of the lateral surface area and the base area:
Surface area = L + B
Surface area ≈ 863.5 + 490.875
Surface area ≈ 1,354.375 square centimeters
Therefore, the surface area of the cone is approximately 1,354.375 square centimeters.