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If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume. NOTE: IT SEEMS THAT r + delta r = 7 but answer comes only by taking initial value r = 7


If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.


NOTE: IT SEEMS THAT r + delta r = 7 but answer comes only by taking initial value r = 7 


Grade:12

4 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

V=(4pi/3)r3, dr=0.02m,,(r+dr)3=(r3+3r2dr+3r(dr)2 +(dr)3)≈r3(1+3(dr/r)) dV=(4pi/3)(3dr/r)=(4pi/3)*3*0.02/7

Gurwinder Kaur
65 Points
10 years ago

as r= 7m   dr = 0.02m 

V = (4pi/3)r3

differentiating both sides

dV = (4pi)/3*3r2dr

=4*22/7*49*0.02

= 15.32m

Hope it is usefull...

then plz don't forget to approve by clicking 'Yes' below....

Godfrey Classic Prince
633 Points
10 years ago

Dear manoj jain,

Given that,

 r = 7m   dr  = 0.02m 

V = (4π/3)r3

Now, differentiating both sides

dV = (4π)/3*3r2dr

=4 * 3.14 * 49 * 0.02

= 15.32m

 

Hope this helped you immensely...

All the Very Best & Good Luck to you dear..

Regards,

AskIITians Expert,

Godfrey Classic Prince

IIT-Madras

Please approve my answer if you liked it by clicking on "Yes" given below...!!Smile

manoj jain
14 Points
10 years ago

according to question initial r is 6.98 or 7.02

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