Question

If the radius of a circle is decreased by 20%, find the percentage decrease in its area.​

Answer 1

36%

Explanation:

Area of circle is

`\pi {r}^(2)`

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

`\pi(0.8r) {}^(2)`

`\pi(0.64 {r}^(2) )`

Since pi is constant, the radius only really matters.

We went from

`1 {r}^(2)`

to

`0.64 {r}^(2)`

So our area will decrease by 36%

Proof: Let the radius be 10.

So the area of circle will be

`\pi(10) {}^(2) = 100\pi`

Let our other radius is 8 because 8 is a 20% decrease of the orginal radius

`\pi(8) {}^(2) = 64\pi`

Next, we subtract the area to find decrease in area

`100\pi - 64\pi = 36\pi`

Since pi is constant, we can ignore it so our decrease in area is 36%