The radius of the base of a cone is 5cm and its slant height is 14cm.Find its curved surface area (π=22 by or upon 7

Question

The radius of the base of a cone is 5cm and its slant height is 14cm.Find its curved surface area (π=22 by or upon 7

Answer 1

Surface Area of the cone is pi*r* ( r + sqrt(h^2 + r^2)) where r is the radius, h is the height, and pi = 22/7

 

By pythagorean , the slant height 14 or hypotneuse is :

 

  14^2 = 5^2 + h^2

 

 196 = 25^2 + h^2

 

 196 - 25 = h^2

 

  171 = h^2

 

  3 * 57 = h^2

 

 3 * 3 * 19 = h^2

 

  3*sqrt(19) = h

 

 

The surface area is then:

  

22/7 * 5 * ( 5 + sqrt(  5^2 +  (3*sqrt(19))^2 ) ) =

 

22/7 * 5 * ( 5 + sqrt( 25 + 171) ) =

 

22/7 * 5 * ( 5 + sqrt( 196)) =

 

22/7 * 5 * (5 + 14) =

 

22/7 * 5 * 19

 

22/7 * 95 =

 

298 and 4/7