McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
Mid-Chapter Quiz
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Exercise 12 Page 840

Use the formulas for the surface area of a cone.

282.7 ft^2

The given solid is a cone.

To calculate the surface area of a cone, we can use the known formula where r is the radius of the base and l is the slant height of the cone. S=π rl+π r^2 To find the slant height, we can use the Pythagorean Theorem. When doing this, the height l is the hypotenuse. The height and the radius of the cone are the legs. By substituting h with 12 and r with 5, we can solve for l.
h^2+r^2=l^2
12^2+ 5^2=l^2
Simplify
144+25=l^2
l^2=144+25
l^2=169
l=13
By substituting r with 5 and l with 13 into the formula, we can now calculate S.
S=π rl+π r^2
S=π( 5)( 13)+π( 5)^2
Simplify right-hand side
S=π(5)( 13)+25π
S=65π+25π
S=90π
S=282.743338...
S≈ 282.7
The surface area of the cone is approximately 282.7ft^2.