A solid cylinder of radius 6 cm & height 15 cm is melted & recast into

1.	A solid cylinder of radius 6 cm & height 15 cm is melted & recast into 12 toys in the shape of right circular cone mounted on hemisphere. Find the radius of hemisphere & the total height of toy if the total height of conical part is thrice it's radius .
Answer» r=6cm h=15cm volume of cylinder= volume of 12 toys volume of cylinder=pi r^2h volume of 12 toys=12(1/3pi r^2h+2/3pi r^3) since h=3r therefore pi r^2h=12(1/3pi 3r^3+ 2/3pi r^3) pi r^2h=12(5pi r^3)/3 pi cancels out r^2h=4x5r^3 36x15=20r^3 r^3=27 r=3 the radius of sphere and cone is 3cm

A solid cylinder of radius 6 cm & height 15 cm is melted & recast into 12 toys in the shape of right circular cone mounted on hemisphere. Find the radius of hemisphere & the total height of toy if the total height of conical part is thrice it's radius .

Answer»

r=6cm h=15cm

volume of cylinder= volume of 12 toys

volume of cylinder=pi r^2h

volume of 12 toys=12(1/3pi r^2h+2/3pi r^3)

since h=3r therefore

pi r^2h=12(1/3pi 3r^3+ 2/3pi r^3)

pi r^2h=12(5pi r^3)/3 pi cancels out

r^2h=4x5r^3

36x15=20r^3

r^3=27

r=3

the radius of sphere and cone is 3cm