Answer:
36%
Step-by-step explanation:
Area of circle is
[tex]\pi {r}^{2} [/tex]
If the radius is decreased by 20%. Then the radius will be
80% of the original radius.
So our radius is 0.8.
So our area is
[tex]\pi(0.8r) {}^{2} [/tex]
[tex]\pi(0.64 {r}^{2} )[/tex]
Since pi is constant, the radius only really matters.
We went from
[tex]1 {r}^{2} [/tex]
to
[tex]0.64 {r}^{2} [/tex]
So our area will decrease by 36%
Proof: Let the radius be 10.
So the area of circle will be
[tex]\pi(10) {}^{2} = 100\pi[/tex]
Let our other radius is 8 because 8 is a 20% decrease of the orginal radius
[tex]\pi(8) {}^{2} = 64\pi[/tex]
Next, we subtract the area to find decrease in area
[tex]100\pi - 64\pi = 36\pi[/tex]
Since pi is constant, we can ignore it so our decrease in area is 36%
