Circle area radius decreased question

Question

I am struggling with this question where I don't know how to use the decrease in the radius to work out how much percentage its radius has decreased.

Question: Question

My working: 10cm - 3cm

= 7cm

7cm/10cm

area difference:

49pi/100pi x 100 to work out percentage

percentage 49%

but the answer is wrong.

Thank You and help is appreciated

Answer 1

You're close. You answered what the area decreased to, not what it decreased by.

Something that decreases to $49\%$ of the original value decreases (or decreases by) $(100 - 49)\% = 51\%$.

Answer 2

HINT

If something goes from $100$ to $49$, it has decreased by $51$

Answer 3

The area of a circle is $A=\pi r^2$. Your original circle had a radius of $10$ cm so that the area was $A_{\text{org}}=\pi 10^2=100\pi$. But now the circle has a radius of $7$ cm so the area is $A_{\text{new}}=\pi 7^2=49 \pi$. The change in area is then $\Delta A=A_{\text{org}}-A_{\text{new}}=100\pi - 49\pi=51\pi$. The percent change in area is then $$\%\Delta=\dfrac{\Delta A}{A_{\text{org}}}=\dfrac{51\pi}{100\pi}=\dfrac{51}{100}=0.51=51\%$$