the area of the ends of the frustumare 183.35 and 103.13 cmsquare if the height of the frustrum is 11 then find the volume of the frustrum

Asked by M.s.srinidhi21 | 26th Sep, 2015, 12:54: PM

Expert Answer:

A r e a space o f space t h e space e n d s space o f space t h e space f r u s t u m space a r e space 183.35 space c m squared space a n d space 103.13 space c m squared space r e s p e c t i v e l y. L e t space R space b e space t h e space b i g g e r space r a d i u s space a n d space r space b e space t h e space s m a l l e r space r a d i u s. T h u s comma space pi R squared equals 183.35 space space c m squared space a n d space pi r squared equals 103.13 space c m squared L e t space straight h space b e space t h e space h e i g h t space o f space t h e space f r u s t u m. space W e space k n o w space t h a t space t h e space v o l u m e space o f space t h e space f r u s t u m equals fraction numerator pi h over denominator 3 end fraction open square brackets straight R squared plus R r plus straight r squared close square brackets space c u b i c space u n i t s space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight h over 3 open square brackets pi R squared plus pi R r plus pi r squared close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight h over 3 open square brackets 183.35 plus pi R r plus 103.13 close square brackets space c m cubed space.... left parenthesis 1 right parenthesis S i n c e space pi R squared equals 183.35 rightwards double arrow straight R squared equals fraction numerator 183.35 cross times 7 over denominator 22 end fraction rightwards double arrow straight R equals square root of fraction numerator 183.35 cross times 7 over denominator 22 end fraction end root... left parenthesis 2 right parenthesis S i m i l a r l y comma space pi r squared equals 103.13 rightwards double arrow straight r squared equals fraction numerator 103.13 cross times 7 over denominator 22 end fraction rightwards double arrow straight r equals square root of fraction numerator 103.13 cross times 7 over denominator 22 end fraction end root... left parenthesis 3 right parenthesis T h u s comma space s u b s t i t u t i j n g space t h e space v a l u e s space o f space straight R space a n d space straight r space f r o m space e q u a t i o n s space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma straight V equals straight h over 3 open square brackets 183.35 plus straight pi open parentheses square root of fraction numerator 183.35 cross times 7 over denominator 22 end fraction end root close parentheses open parentheses square root of fraction numerator 103.13 cross times 7 over denominator 22 end fraction end root close parentheses plus 103.13 close square brackets rightwards double arrow straight V equals straight h over 3 open square brackets 286.48 plus 137.51 close square brackets rightwards double arrow straight V equals 11 over 3 cross times 423.99 rightwards double arrow straight V equals 1554.63 space c m cubed

Answered by Vimala Ramamurthy | 26th Sep, 2015, 04:35: PM

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