Question

A circle of a certain radius has an area which is numerically 5 times the value of the circumference. What is the radius of the circle?

Answer 1

We have been given that a circle of a certain radius has an area which is numerically 5 times the value of the circumference. We are asked to find the radius of the circle.

We know that area of circle with a radius of r units is
`\pi r^2`.

We know that circumference of a circle is
`2\pi r`.

5 times the value of circumference would be
`5(2\pi r)=10\pi r`.

Now we will equate 5 times circumference with area as:

`\pi r^2 = 10\pi r`

Let us solve for r.

`\pi r\cdot r = 10\pi r`

`(\pi r\cdot r)/(\pi r)=(10\pi r)/(\pi r)`

`r=10`

Therefore, the radius of the circle would be 10 units.