Question

A circle has a radius r which is a positive integer. If the circumference of the circle divided by the area of the circle is a prime number, what is the sum of all possible values for the radius of the circle?

Answer 1

The possible value for the radius of the circle is 1 unit

Area and Circumference of a circle

The formula for calculating the area of a circle is expressed as:

• A = πr²

The formula for calculating the circumference is expressed as:

• C = 2πr

where r is the radius of the given circle.

If the circumference of the circle divided by the area of the circle is a prime number, then;

$\frac{2 \pi r}{\pi r^2} = p\\\frac{2}{r} = prime$

For the value to the prime and r to be an integer, the possible value for the radius of the circle is 1 unit

Learn more on circles here: brainly.com/question/402655