Question

The surface area of a sphere of radius 5 cm is five times the curved surface area of a cone of radius 4 cm. Find the height of the cone.

Answer 1

Let R be the radius of the sphere and r be the radius of the cone
4π$R^{2}$=5πrl
l=4*R*R/5r
l=4*5*5/4*5
l=5cm

[tex] l= \sqrt{ h^{2}+ r^{2} } [/tex]
h=[tex] \sqrt{ l^{2} - r^{2} } [/tex]
h=$\sqrt{ 5^{2}-4^{2} }$
h=√9=3cm
∴The height of the cone is 3cm