by what percent does the area increase if the radius is increased by 10%?

Question

A = f (r) = the area of a circle of radius r

Answer 1

If the radius is multiplied by 1.1, then the area is multiplied by 1.1^2 = 1.21. That is an increase of 21%.

Answer 2

For a circle, the Area = (pi)*r^2

if r=1, then A = pi. If r=1.10 (10% increase), then A = 1.21(pi).

Therefore, the area increases by 21%.

Pi is a constant, so it doesn't matter. The change in area is essentially (1.1)*(1.1) = 1.21

Answer 3

Original radius = 1.00
Area is proportional to radius squared.
New radius = 1.10
1.10^2 = 1.21
21%
New area is greater by 21%

Answer 4

If the radius increases by 10%:

A = pi * (1.1r)^2 = 1.21 pi*(r^2)

Answer 5

Area is proportional to r^2

Thus if you increase r to 1.1r

Then r^2 goes to 1.21r^2

Or the percent increase is 21%

Answer 6

f(r)=pi(r)^2

if you increase by 10% the radius then take r to be 1.10r

f(1.10r)=pi(1.10r)^2= 1.21pi(r)^2

that is 21%