Question

By what percentage must the diameter of a circle be increased to increase its area by 50%?

Answer 1

The area of a circle is:
 A = pi * (d / 2) ^ 2
 A = (1/4) * pi * (d) ^ 2
 Where,
 d: diameter of the circle.
 By clearing the diameter we have:
 D = sqrt (4A / pi) if the area increases 50% we have:
 D '= sqrt (4 * (1.5 * A) / pi)
 Rewriting:
 D '= sqrt (1.5) * sqrt (4 * A / pi) = sqrt (1.5) * D
 The new diameter is:
 D '= sqrt (1.5) * D
 The percentage increase is:
 [sqrt (1.5) -1] * 100% = 22.47%
 Answer:
 The diameter of a circle must be increased 22.47% to increase its area by 50%