Question

If the area of the base of a right circular cone is 3850 cm² and its height is 84 cm, then find the slant height of the cone.

Answer 1

We have,

Height = 84 cm 

Let the radius and the slant height of the cone be r and l, respectively.

Area of the base of the cone = 3850 cm²  

`=> pi"r"^2 = 3850`

`=> 22/7xx"r"^2 = 3850`

`=> "r"^2 = 3850xx7/22`

`=> "r"^2 = 1225`

`=> "r" = sqrt(1225)`

∴ r = 35 cm

Now,

`"l" =sqrt("h"^2+"r"^2)`

`=sqrt(84^2+35^2)`

`=sqrt(7056+1225)`

`=sqrt(8281)`

= 91 cm

So, the slant height of the given cone is 91 cm.