A solid hemisphere of radius 24 cm is melted and identical cones each of base radius 8 cm and height 6 cm are formed. How many such cones are formed?
Answer & explanation
Correct answer: option 3
radius of hemisphere = 24 cm
volume of hemisphere = 2Π(r^3)/3 = 2Π(24^3)/3
n number Cones are formed after melting the hemisphere
radius of cone = 8 cm
height = 6 cm
volume of 1 cone = Π(r^2)*h/3 = Π(8^2)*6/3
Also, volume of n cones = Volume of hemisphere
n * Π(8^2)*6/3 = 2Π(24^3)/3
n * 8 * 8 * 2 = 2 * 24 * 24 * 24 /3
n = 3*3*8 = 72
The correct answer is Option (3) → 72