Mathematics [ use Binomial approximation ]?

Question

Question

determine the approximation error in calculating the volume V and surface area A of a sphere if the radius r of the sphere is measured 1.5% too large.

Answer 1

V=4/3*(pi*r^3)

>dV=4*pi*r^2*dr

dr=0.015*r

>dV=4*pi*r^3*0.015

>dV=3*V*0.015

>dV/V=3*0.015=0.045=4.5%

Similarly..

dA=8*pi*r*dr=8*pi*r^2*0.015= 4*pi*r^2*0.03

>dA/A=0.030=3%

Answer 2

do it the hard way.

V₁ = ⁴/₃πr³

V₂ = ⁴/₃π(1.015r)³

V₂ = ⁴/₃πr³(1.0457)

V₂/V₁ = 1.0457

error is 4.57%

simple method: 3*1.5% = 4.5%

Answer 3

volume of a sphere is 4/3 pi r^3

r is 1.5% too large. Correct volume is

(98,5/100 * r^)3 * 4/3* Pi