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CBSE Class 9 Answered

A cone is 8.4cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. Find the radius of the sphere
Asked by valeen_sodhi | 14 Mar, 2016, 09:32: PM
answered-by-expert Expert Answer
L e t space t h e space r a d i u s space o f space t h e space c o n e space b e space r subscript c space a n d space t h e space r a d i u s space o f space t h e space s p h e r e space b e space r subscript s.
V o l u m e space o f space t h e space c o n e space equals space V o l u m e space o f space t h e space s p h e r e space. space. space. space left parenthesis S i n c e space t h e space c o n e space h a s space b e e n space m e l t e d space a n d space r e c a s t e d space i n t o space a space s p h e r e. right parenthesis
rightwards double arrow 1 third pi r subscript c squared h space equals space 4 over 3 pi r subscript s cubed
rightwards double arrow fraction numerator 1 over denominator up diagonal strike 3 end fraction up diagonal strike pi r subscript c squared h space equals space fraction numerator 4 over denominator up diagonal strike 3 end fraction up diagonal strike pi r subscript s cubed
rightwards double arrow fraction numerator 2.1 cross times 2.1 cross times begin display style stack up diagonal strike 8.4 end strike with 2.1 on top end style over denominator begin display style stack up diagonal strike 4 with 1 below end style end fraction equals r subscript s cubed
rightwards double arrow 2.1 space cross times space 2.1 space cross times space 2.1 space equals space r subscript s cubed
rightwards double arrow r subscript s equals 2.1 space. space. space. space. space left parenthesis T a k i n g space c u b e space r o o t space o n space b o t h space s i d e s. right parenthesis
H e n c e comma space r a d i u s space o f space t h e space s p h e r e space i s space 2.1 space c m.
Answered by Rebecca Fernandes | 15 Mar, 2016, 10:26: AM

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