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.

$\pi r\cdot r = 10\pi r$

$\frac{\pi r\cdot r}{\pi r}=\frac{10\pi r}{\pi r}$

$r=10$

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