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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Chapter Review

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Exercise 16 Page 753

Use the formula for the surface area of a cone.

185.6 ft^2

Practice makes perfect

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 We can see that the length of radius is 4ft. To find the slant height, we can use the Pythagorean Theorem. When doing this, the slant height l is the hypotenuse. The height of the cone and radius of the base are the legs. Let's use these given values to solve for l.

r^2+h^2=l^2

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Solve for l

r= 4, h= 10

4^2 + 10^2 = l^2

Calculate power

16 + 100 = l^2

Add terms

116 = l^2

sqrt(LHS)=sqrt(RHS)

sqrt(116) = l

Rearrange equation

l = sqrt(116)

The length of the slant height is sqrt(116). Now we have all the information we need to calculate the surface area of the cone. By substituting r with 4 and l with sqrt(116) into the formula, we can calculate S. Let's do it!

S=π rl+π r^2

r= 4, l= sqrt(116)

S=π( 4)( sqrt(116))+π( 4)^2

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Simplify right-hand side

Calculate power

S=π(4sqrt(116))+16π

Factor out π

S=(16+4sqrt(116))π

Use a calculator

S=185.60943...

Round to 1 decimal place(s)

S≈ 185.6

The surface area of the cone, to the nearest tenth, is 185.6ft^2.