Question

The surface area of a sphere of radius 5cm is five times the curved Surface area of cone of radius4 cm. Find the height of the cone.

Answer 1

Solution:-
Let the radius of sphere be 'R'
and, the radius of the cone be 'r' and height be 'h' respectively.
Surface area of the sphere = 4πr²
= 4π(5)²
= 4π(25)
100π cm²
Curved surface area of the cone = πrl
= π*4*l
= 4πl cm²
Given that the surface area of the sphere is 5 times the curved surface area.
∴ 100π cm² = 5 × 4πl cm²
100π cm² = 20πl cm²
l = 100/20
l = 5 cm = Slant height of he cone.
Now,
l = √r²+h²
(5²) = √(4)²+(h)²
h² = 25 - 16
h = √9
h = 3 cm
Height of the cone is 3 cm.
Answer.