Question

A hemisphere of lead of radius 7 cm is cast into a cone of base radius 3.5 cm. Find the height of the cone.

Answer 1

Hi !

Radius of the hemisphere  = r = 7 cm
Volume of the hemisphere = 2/3 πr³
                                           = 2/3 * 22/7*7*7*7
                                           = 718.67
                                           = 718 cm³ ( approx.)

Radius of cone = 3.5 cm
Volume of cone = 1/3 πr²h
                          = 1/3*22/7*(3.5)²*h

volume of  cone = volume of hemisphere
 1/3*22/7*(3.5)²*h = 718
12.833 *h = 718

12.833 is taken as 13 ( for easy calculation)

13*h = 718

h = 718/13
   = 55.23 cm

Height of cone = 55.23 cm