The area of circle is 100 times the area of another circle. What is th

1.	The area of circle is 100 times the area of another circle. What is the ratio of their circumferences?
Answer» Let the area of the circles be A₁ and A₂ and their circumference be c₁ and c₂respectively. According to the question it is clear that A₁ = 100 A₂ ⇒ π (r₁)² = 100 × π (r₂)² ⇒ r₁ = 10 r₂ ⇒ r₁/r₂ = 10/1 … (i) Finding the ratios of the circumference; C₁: C₂ = 2πr₁: 2πr₂ C₁/C₂ = (2πr₁)/ (2πr₂) C₁/C₂ = r₁/r₂ Putting the value of r₁/r₂from equation (i) C₁/C₂ = 10/1 C₁: C₂ = 10: 1 Hence, the ratio of their circumferences is 10: 1.

The area of circle is 100 times the area of another circle. What is the ratio of their circumferences?

Answer»

Let the area of the circles be A₁ and A₂ and their circumference be c₁ and c₂respectively.

According to the question it is clear that A₁ = 100 A₂

⇒ π (r₁)² = 100 × π (r₂)²

⇒ r₁ = 10 r₂

⇒ r₁/r₂ = 10/1 … (i)

Finding the ratios of the circumference;

C₁: C₂ = 2πr₁: 2πr₂

C₁/C₂ = (2πr₁)/ (2πr₂)

C₁/C₂ = r₁/r₂

Putting the value of r₁/r₂from equation (i)

C₁/C₂ = 10/1

C₁: C₂ = 10: 1

Hence, the ratio of their circumferences is 10: 1.