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Art [367]
3 years ago
12

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?
Mathematics
1 answer:
patriot [66]3 years ago
5 0

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.

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