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The surface area of a cone is 500pi the height is 15 what is the area of the base.

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the formula for surface area is pi times radius times slant height plus pi times radius squared.

asked Feb 17, 2014 in GEOMETRY by johnkelly Apprentice

1 Answer

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Given that :

Surface area of a cone (S ) = πr (r +√(r ^2 + h ^2)) =  500π square units.

Height (h ) = 15 units.

Substitute h = 15 in πr (r +√(r ^2 + h ^2)) =  500π

πr (r  + √(r ^2 + h ^2)) =  500π

r (r  + √(r ^2 + h ^2)) = 500

r ^2 + r √(r ^2 + 225) = 500

r ^2 + r √(r ^2 + 225) = 500

r √(r ^2 + 225) = 500 - r ^2

Squring on both sides.

[r √(r ^2 + 225)]^2 = [500 - r ^2]^2

r ^2(r ^2 + 225) = r ^4 - 1000r ^2 + 250000

r ^4 + 225r ^2 - r ^4 + 1000r ^2 = 250000

1225r ^2 = 250000

r ^2 = 250000/1225 = 10000/49

r = ± 100/7

The base of the cone is circle, so radius of circle is (r ) = 100/7 units.

Area of the base (A ) = πr ^2.

Substitute r = 100/7 and π = 3.14.

A = 3.14 * (100/7)^2

   = 640.63.

Therefore, area of the base is 640.63 square units.

answered Apr 1, 2014 by lilly Expert

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