Circle Problem in mathematics

Question

DanTyro

Asked: April 21, 20212021-04-21T02:17:06+00:00 2021-04-21T02:17:06+00:00In: Middle School/Junior Secondary School

If the radius of a circle is decreased by 10%., by what percent is its area decreased?

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acedstud · Answer 1 · 2021-04-21T17:33:14+00:00

acedstud

This answer was edited.

The area, $A$ , of a circle of radius, $r$ , is given by $A=\pi r^2$ .

When the radius is decreased by 10%, the new radius is $\dfrac{100\%-10\%}{100\%}r=\dfrac{90\%}{100\%}r=0.9r$ .

Then, the new area is $A=\pi (0.9r)^2=0.81\pi r^2=0.81\times\text{ area of the original circle}$ .

Therefore, the new area is an 100% – 81% = 19% decrease from the original area.

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