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ICSE Class 10 Answered

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere. Justify it. 
Asked by jaiswalsindhuli717 | 20 Oct, 2018, 12:10: PM
answered-by-expert Expert Answer
Volume of sphere = begin mathsize 16px style 4 over 3 πr cubed end style
Volume of cylinder = begin mathsize 16px style πr squared straight h end style
According to the question,
h = d and r = d/2
r2 = d2/4 and r3 = d3/8
begin mathsize 16px style fraction numerator Volume space of space sphere over denominator Volume space of space cylinder end fraction equals fraction numerator begin display style 4 over 3 straight pi straight d cubed over 8 end style over denominator straight pi straight d squared over 4 cross times straight d end fraction equals fraction numerator begin display style 4 end style over denominator begin display style 3 end style end fraction straight pi fraction numerator begin display style straight d cubed end style over denominator begin display style 8 end style end fraction cross times 4 over πd cubed equals 2 over 3 end style
Hence, it is proved.
Answered by Sneha shidid | 22 Oct, 2018, 11:24: AM

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