Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
3. Surface Areas of Pyramids and Cones
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Exercise 44 Page 715

Use the formula for the surface area of a cone.

A

Practice makes perfect
The given solid is a cone. To calculate the surface area of a cone, we can use the formula where r is the radius of the base and l is the slant height of the cone. S.A.=π rl+π r^2We know that the diameter of the cone's base is 27m. By dividing it by 2, we get the radius of the base. r=27/2=13.5m We are told that the slant height of the cone equals 19m. By substituting r=13.5 and l=19 into the formula, we can calculate the surface area of the cone.
S.A.=π rl+π r^2
S.A.=π( 13.5)( 19)+π( 13.5)^2
Simplify right-hand side
S.A.=π(13.5)( 19)+182.25π
S.A.=256.5π+182.25π
S.A.=438.75π
S.A.=1378.373776...
S.A.≈ 1378
The surface area of the cone is approximately 1378 square meters. This means that the correct answer is A.