bake a pie for 4 people. you know baking a pie for 9 people, a radius of 12cm gives you the perfect amount. what is the radius for the 4 person pie

Question

You need to bake a pie for $4$ people; you know that if you bake a pie for $9$ people with a radius of $12~\mathrm{cm}$ you have the perfect amount of pie. What radius pie should you bake for $4$ people, assuming both pies are the same thickness?

So in my head, I'm thinking if I have the area of the pie for $9$ people $A= \pi(12)^2 = 452.16$ and take the area and divide by $9$ for the amount for each person $= 50.24$
then I can multiply that number by $4$ and work backwards to find the radius of the $4$ people pie? would give me $8$ as the radius of the $4$ people pie.

Is this line of thinking correct or am I missing something?

Answer 1

It's simpler (and more accurate) to keep $\pi$ in the calculation rather than multiplying it out:

$A=\pi(12)^2=144\pi$
Divide by $9$ to get $16\pi$
Multiply by $4$ to get $64\pi$, which is $\pi(8)^2$

So the answer is $8$cm.

Answer 2

You are right. But it's much simpler to think in terms of similarity. All circles are similar to one another, so the radius defines the exact size. The ratio of areas of two circles is the square of the ratio of radii. So the radius of the smaller pie you want is $12\sqrt{\frac 49} = \frac 23(12) = 8 \mathbb{cm}$.