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

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 %

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%