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

Question

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

Answer 1

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.