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CBSE Class 10 Answered

A solid cylinder of diameter 12 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 hemispphere and the total height of the toy if height of the cone is 3 times the radius.
Asked by Aleena | 14 Mar, 2015, 10:26: AM
answered-by-expert Expert Answer

hi aleena,v o l u m e space o f space c y l i n d e r space equals space 12 space cross times space v o l u m e space o f space t o y v o l u m e space o f space c y l i n d e r space equals space 12 left parenthesis v o l u m e space o f space c o n e plus v o l u m e space o f space h e m i s p h e r e right parenthesis πr squared straight h space equals space 12 cross times open parentheses 1 third cross times straight pi cross times straight r subscript 1 squared cross times straight h space space space plus space space space 2 over 3 cross times straight pi cross times straight r subscript 1 cubed close parentheses space space space space space left parenthesis radius space of space cone space equals space radius space of space hemisphere right parenthesis straight r squared straight h space equals space 12 over 3 cross times straight r subscript 1 squared cross times 3 straight r space space space plus space space 12 cross times 2 over 3 cross times straight r subscript 1 cubed straight r squared straight h space equals space 20 straight r subscript 1 cubed 6 cross times 6 cross times 15 equals space 20 cross times straight r subscript 1 cubed straight r subscript 1 cubed space equals space 27 r subscript 1 equals space 3 c m h space equals space 3 cross times r equals space 3 cross times 3 equals space 9 c m r a d i u s equals space 3 c m h e i g h t equals space 9 c m

Answered by | 16 Mar, 2015, 06:41: PM

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