Question

A solid cylinder of diameter 12 cm and height 15 cm is melted and
Frecast 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 of
the toy, if the height of the conical part is thrice its radius.​

Answer 1

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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