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A sphere and a right circule cylinder of the same radius have equal volume. By what percentage does the diameter of the cylinder exceed its height ? |
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Answer» Let the radius of sphere= r= Radius of a right circular cylinder According to the question, Volume of cylinder= volume of a sphere `rArr " "pir^(2) h = (4)/(3) pir^(3) rArr h = (4)/(3) r` `because` Diameter of the cylinder = 2r `therefore`Inreased diameter from height of the cylinder `= 2r-(4r)/(3) = (2r)/(3)` Now,percentage increase in diameter of the cylinder `= (((2r)/(3) xx100))/((4)/(3)r) = 50%` Hence, the diameter of the cylinder exceeds its height by 50%. |
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