Question

A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into 12 toys in the shape of aright circular cone mounted on a hemisphere. Find the radius of the hemisphere and total height ofthe toy, if the height of the cone is 3 times the radius

Answer 1

Step-by-step explanation:

Let the number of toys formed be 'n', then

n× vol. of each toy=vol. of cylinder

⇒n×[

3

1

π×3

2

×9+

3

2

π×3

3

]=π×6

2

×15

⇒n×

3

π

[81+54]=π×36×15

⇒n=

135

36×15×3

=12

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Answer 2

Answer:

Let the number of toys formed be 'n', then

n× vol. of each toy=vol. of cylinder

⇒n×[

3

1

π×3

2

×9+

3

2

π×3

3

]=π×6

2

×15

⇒n×

3

π

[81+54]=π×36×15

⇒n=

135

36×15×3

=12