a solid cylinder of diameter 15 cm and height 15 cm is melted and recast into 12 toys in the shape of a right circular cone mounted on a hemisphere find the radius of the hemisphere and the total height too. if height of the conical part is 3 times its radius
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in cylinder
diameter is 12 cm
hence radius will be 6cm
height is 15 cm
volume of cylinder is
πr^2h
π ×6×6×15 cm ^3
now, volume of 1 toy
2/3 × πr^3 + 1/3 πr^2 h
1/3 πr^2 ( 2r + h)
height of cone is 3 times r
h = 3r
as 12 toys were recasted..
volume of 12 toys = volume of cylinder
12 ×1/3 πr^2 ( 2r + h) = πr^2h
4 πr^2 ( 2r + 3r ) = π ×6×6×15
4 r^2 (5r) = 6×6×15
r^3 = 6 ×6×15/4×5
r ^3 = 3 ×3×3
r = 3 cm
radius of sphere is 3 cm
height of conical part is 3 ×3 = 9 cm
height of toy is 3 +9 = 12 cm
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