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CBSE Class 12-science Answered

Find out the approximate error in the surface area of a sphere where the radius was measured by mistake with an error of 0.05 cm as 10 cm.
Asked by Topperlearning User | 05 Aug, 2014, 02:40: PM
answered-by-expert Expert Answer

If r is the radius, then

r=10 cm and Δr=0.05 cm 

Volume of the sphere is

V equals 4 over 3 πr cubed

On differentiating with respect to radius

fraction numerator d v over denominator d r end fraction equals 4 πr squared rightwards double arrow dv equals open parentheses dv over dr close parentheses increment straight r space space space space space space space space space equals 4 straight pi left parenthesis 10 right parenthesis squared cross times 0.05 space space space space space space space space space equals 20 straight pi space cm cubed  

Approximate error in the surface area of the sphere=20 v∏ cm3

Answered by | 05 Aug, 2014, 04:40: PM

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