It is known that the area of a circle is directly proportional to the square of the radius.

(a) By how many percent will the area of a circle increase if its radius is increased by 50%?
(b) If we wish to halve the area of a circle, what should be done with its radius?

Question

It is known that the area of a circle is directly proportional to the square of the radius.

(a) By how many percent will the area of a circle increase if its radius is increased by 50%?
(b) If we wish to halve the area of a circle, what should be done with its radius?

cwrw238 · Answer

if iniital radius is 1x the 50% increase makes it 1.5x
initial area = 1x^2  will increase to  2.25x^2

so increase is 1.25   or 125%