Question

The radius of a sphere is measured with an error of 10%. What would be the % error in volume

Answer 1

V= 4/3 pie r^3

dv/dr = 4/3 pie × 3 r^2

dv/dr = 4 pie r^2

dr/r = 10/100 = 1/10

dv/v = dv/4/3 pie r^3

= 3 dv/ 4 pie r^3

Now

dv/dr × dr/r = dv/r = 4pie r^2 × 1/10

= 2 pie r^2/5

So dv /r = 2 pie r^2/5

dv/r^3 = 2 pie /5

Now dv/v = 3 /4 pie. × dv/r^3

= 3/4 pie. × 2 pie /5

= 3/10

dv/v × 100 = 3× 100/10= 30%