CBSE Class 10 Answered

A metallic right circular cone 20 cm high and whose vertical angle is 600 is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/16 cm, find the length of the wire. 2morw exam pls help asap

Asked by Vampire S. | 15 Mar, 2015, 18:49: PM

Expert Answer

$C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.$

$triangle A B C space a n d space triangle A D E space a r e space s i m i l a r space t r i a n g l e s space a n d h e n c e space t h e space c o r r e s p o n d i n g space s i d e s space a r e space p r o p o r t i o n a l. B space i s space t h e space m i d p o i n t space o f space A D. T h u s comma space fraction numerator A B over denominator A D end fraction equals fraction numerator B C over denominator D E end fraction L e t space r space a n d space R space b e space t h e space r a d i i space o f space t h e space b o t h space t h e space e n d s space o f space t h e space f r u s t u m. T h u s comma space w e space h a v e comma 10 over 20 equals r over R rightwards double arrow R equals 2 r A l s o space c o n s i d e r space t h e space t r i a n g l e comma space triangle A D E tan 30 degree equals fraction numerator o p p over denominator a d j end fraction equals fraction numerator 1 over denominator square root of 3 end fraction equals R over 20 rightwards double arrow R equals fraction numerator 20 over denominator square root of 3 end fraction space c m rightwards double arrow r equals fraction numerator 10 over denominator square root of 3 end fraction space c m V o l u m e space o f space t h e space f r u s t u m equals straight pi over 3 open square brackets R squared plus R r plus r squared close square brackets h straight pi open parentheses fraction numerator begin display style 1 over 16 end style over denominator 2 end fraction close parentheses squared cross times straight h equals straight pi over 3 open square brackets 400 over 3 plus 200 over 3 plus 100 over 3 close square brackets cross times 10 rightwards double arrow 1 over 1024 cross times h equals 1 third open square brackets 900 over 3 close square brackets cross times 10 rightwards double arrow 1 over 1024 cross times h equals 100 cross times 10 rightwards double arrow 1 over 1024 cross times h equals 1000 rightwards double arrow h equals 1000 cross times 1024 space c m rightwards double arrow h equals 10240 space m$