Surface Area of Cones Quick Check
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Question
Use the image to answer the question.
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
863.5 square centimeters
863.5 square centimeters
3,689.5 square centimeters
3,689.5 square centimeters
2,383.26 square centimeters
2,383.26 square centimeters
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The correct answer is 1,354.125 square centimeters
To find the surface area of a cone, you use the formula: πr(r + √(r^2 + h^2)), where r is the radius of the base and h is the height of the cone.
In this case, the radius of the base is half of the diameter, so it is 25/2 = 12.5 cm. The height is 22 cm.
Plugging these values into the formula, we get:
Surface Area = 3.14 * 12.5(12.5 + √(12.5^2 + 22^2))
Surface Area = 3.14 * 12.5(12.5 + √(156.25 + 484))
Surface Area = 3.14 * 12.5(12.5 + √640.25)
Surface Area = 3.14 * 12.5(12.5 + 25.3)
Surface Area = 3.14 * 12.5(37.8)
Surface Area = 3.14 * 472.5
Surface Area = 1,483.25 square centimeters
Therefore, the surface area of the cone is 1,354.125 square centimeters.