Question

The area of a circle is 100 times thr area of another circle. What is the ratio of their circumference

Answer 1

Area of Circle C1= πR² = 100

Area of Circl C2= πr² = 1

C1/C2 = πR²/πr²

πR²/πr² = 100/1

R²/r² = 10/1

R:r = 10:1

Answer 2

ANSWER:-

Given:

The area of a circle is 100 times the area of another circle.

To find:

The ratio of their circumference.

Explanation:

We know that formula of the area of circle: πr² sq. unit

$\frac{A1}{A2}= 100$

Therefore,

$\frac{\pi r1^{2} }{\pi r2^{2} } =100\\\\\frac{r1^{2} }{r2^{2} } =100\\\\\sqrt{\frac{r1^{2} }{r2^{2} } } =\sqrt{100} \\\\\frac{r1}{r2}= 10$

Now,

Ratio of circumference: 2πr1 : 2πr2

⇒ $\frac{2\pi r1}{2\pi r2} =10$

⇒ $\frac{r1}{r2} =10$

Thus,

The ratio of circumference is r1: r2= 10:1