A solid cylinder of base radius 12 cm and height 15 cm is melted and recast into n toys each in shape of right circular cone of height 9 cm mounted on a hemisphere of radius 3cm. The value of n is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is 1 i.e. 48
Volume of cylinder =π r²h
= π x 12² x 15 = 2160π
Volume of n right circular cone = (1/3) π r² h x n
= (1/3) x 9 x 9 x n = 27π x n
Volume of hemisphere = (2/3) π x (3)² x n
=(2/3)π x 9 x 3 x n =18π x n
2160π =(27π x n)+ (18π x n)
2160 = n (27 + 18)
n = 2160/45
n = 48