Question

There are two concentric circles with radii 10 and 8. If the radius of the outer circle is increased by 10% and the radius of the inner circle decreased by 50%, approximately by what percent does the area between the circles grow?

Answer 1

The area between the circles grow at 192%.

Explanation:

Consider the provided information.

There are two concentric circles with radii 10 and 8.

Area between the two circles = π×10²−π×8²

π×(10²−8²)=π×(100-64)

π×(36)=36π

If the radius of the outer circle is increased by 10% and the radius of the inner circle decreased by 50%,

10% of 10 is 1. Thus the new radius of bigger circle is 10+1=11.

50% of 8 is 4. Thus the new radius of the smaller circle is 8-4=4.

Area between the two circles upon change in Radii is

π×(11²−4²)=π×105

Change in area is 105π-36π = 69π

%change in Area=(Change in Area/Original Area)×100

Substitute the respective values in the above formula.

`(69\pi)/(36\pi)*100`

`1.92*100`

`192\%`

Hence, the area between the circles grow at 192%.