Surface Area of Cones Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Use the image to answer the question.
A cone shows a radius of 6 and hypotenuse or side as 11.
What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
(1 point)
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To find the surface area of a cone, you can use the formula:
Surface Area = πr^2 + πr√(r^2 + h^2)
Given the radius (r) = 6 and the side or hypotenuse (h) = 11, we can first find the height using the Pythagorean theorem:
h^2 = 11^2 - 6^2
h^2 = 121 - 36
h^2 = 85
h = √85
Now, plug in the values into the formula:
Surface Area = 3.14(6^2) + 3.14(6)√(6^2 + 85)
Surface Area = 3.14(36) + 3.14(6)√(36 + 85)
Surface Area = 113.04 + 3.14(6)√121
Surface Area = 113.04 + 18.84(11)
Surface Area = 113.04 + 207.24
Surface Area = 320.28
Therefore, the surface area of the cone is 320.3 (rounded to the nearest tenth).