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CBSE Class 9 Answered

IF THE RADIUS AND HEIGHT OF A CONE BOTH ARE INCREASED BY 10%,THEN THE VOLUME OF THE CONE IS INCREASED BY:
Asked by vaishnavi | 04 Apr, 2016, 01:46: PM
answered-by-expert Expert Answer
Let space the space radius space and space height space of space the space cone space be space straight r space and space straight h space respectively.
So space volume space of space the space cone space equals 1 third πr squared straight h
The space new space radius space of space the space cone space is space straight r plus 1 over 10 straight r equals 11 over 10 straight r
The space new space height space of space the space cone space is space straight h plus 1 over 10 straight h equals 11 over 10 straight h
So space volume space of space the space new space cone space equals 1 third straight pi open parentheses 11 over 10 straight r close parentheses squared open parentheses 11 over 10 straight h close parentheses equals 1 third πr squared straight h open parentheses 11 over 10 close parentheses cubed
percent sign space increase space in space volume space of space cone
equals space fraction numerator 1 third πr squared straight h open parentheses 11 over 10 close parentheses cubed minus 1 third πr squared straight h over denominator 1 third πr squared straight h end fraction cross times 100
equals space fraction numerator 1 third πr squared straight h open square brackets open parentheses 11 over 10 close parentheses cubed minus 1 close square brackets over denominator 1 third πr squared straight h end fraction cross times 100
equals space open square brackets open parentheses 11 over 10 close parentheses cubed minus 1 close square brackets cross times 100 space equals space open square brackets 1331 over 1000 minus 1 close square brackets cross times 100 space equals space 0.331 cross times 100 equals 33.1 percent sign
Answered by Rebecca Fernandes | 04 Apr, 2016, 02:03: PM
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