Question

The radius of a circle is increased from 6.00 to 6.06.
Estimate the resulting change in​ area, and then express the estimate as a percentage of the​ circle's original area.

Answer 1

Answer:

a) Change in area = 0.72π m²

b) Estimated change in %age = 2%

Step-by-step explanation:

$Initial\,\, radius = r = 6 m\\\\Final \,\,radius = r_1 = 6.06 m\\\\Change\,\, in\,\,radius = dr =6.06 - 6 = .06 m$

$Area\,\,of\,\,circle= A=\pi r^2\\\\A=36\pi \,m^2\\\\Chang\,\, in\,\, area = dA= 2\pi r.dr\\\\dA=2\pi(6)(.06)\\\\dA=0.72\pi\,m^2\\\\Estimated\,\, \%age\,\, change=\frac{0.72\pi}{36\pi}\times 100\%\\\\=2\%$