Question

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

Answer 1

The area is to be increased by 50%.

Area of the circle is given by: A = πr²

New Area = A' = A + 50% of A = 1.5 A 
Let the new radius be R.

So, we can say:

A' = πR² = 1.5 πr²
⇒

R² = 1.5r²
⇒
R = √1.5 r

This shows that the radius must be increased to square root of 1.5 times to increase the Area by 50%.

Diameter is the twice of radius, so the change in diameter will also be the same i.e square root of 1.5 times.

So, diameter must be made 1.225 times. In percentage this can expressed as 22.5%.

Hence, the answer to this question is 22.5%

Answer 2

The circle increase in area will be by a factor of 1.5
So corresponding increase in the diameter will be a factor of  sqrt 1.5 = 1.2247

Answer is 22.47 %