Question

The area of a circle is directly proportional to the square of its radius. If the radius is halved, by what factor is the area multiplied? a) 1/8 b) 2 c) 1/2 d) 4 e) 1/4

Can you deeply and clearly explain to me, please? Thanks.

Answer 1

A=pi r^2?

Answer 2

\[\bf A=\pi r^2\]If we take half the radius, the area becomes:\[\bf A=\pi \left( \frac{ r }{ 2 } \right)^2=\pi \frac{ r^2 }{ 4 }\]Looking at the work above, can you tell me what the answer would be? @arianneee

Answer 3

Would it be 1/4? Wait, am I wrong?

Answer 4

@arianneee That is correct. You can clearly see that the "pir^2" gets multiplied by 1/4 when the radius is halved. So you are fine =).