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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
3,689.5 square centimeters
3,689.5 square centimeters
863.5 square centimeters
863.5 square centimeters
1,354.125 square centimeters
1,354.125 square centimeters
2,383.26 square centimeters
2,383.26 square centimeters
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To calculate the surface area of a cone, you need to find the area of the base and the area of the curved surface.
First, find the radius of the base using the given diameter: radius = diameter/2 = 25 cm / 2 = 12.5 cm.
Now, the area of the base (which is a circle) can be calculated using the formula for the area of a circle: A = πr^2 = 3.14*(12.5)^2 = 3.14*156.25 = 490.625 square centimeters.
The curved surface area of the cone can be calculated using the formula: A = πr*l, where l is the slant height of the cone.
First, let's find the slant height using the Pythagorean theorem: r^2 + h^2 = l^2, where r is the radius and h is the height.
12.5^2 + 22^2 = l^2
156.25 + 484 = l^2
640.25 = l^2, so l = √640.25 ≈ 25.3 cm.
Now, calculate the curved surface area: A = 3.14*12.5*25.3 ≈ 992.95 square centimeters.
Finally, add the base area and curved surface area to get the total surface area: 490.625 + 992.95 ≈ 1483.575 square centimeters.
Using the closest option listed, the surface area of the cone is 1,354.125 square centimeters.