Question

If the ratio of the diameter of two circles is 2:5, find the ratio of their circumferences. ​

Answer 1

Step-by-step explanation:

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Answer 2

Given,

The given ratio of the diameter of two circles is 2:5.

To find,

The ratio of their circumference.

Solution,

The circumference of a circle is known as the length of the complete arc of a circle The formula of the circumference of a circle is given as, C = 2πr.

r is known as the radius of the circle and it is half of the diameter of the circle.

Since the ratio of the diameter of two circles is 2:5.

Let the diameter of the first circle = 2x.

Hence, the radius of the first circle = d/2 ⇒ 2x/2 = x.

Therefore the circumference of first circle-

⇒  C1 = 2πr

⇒  C1 = 2π(x)

⇒ C1 = 2πx

Let the diameter of the second circle = 5x.

Hence, the radius of the first circle = d/2 ⇒ 5x/2.

Therefore the circumference of the second circle-

⇒   C2 =  2πr

⇒   C2 = 2π(5x/2)

⇒   C2 = 5πx.

Hence the ratio of the circumferences of the circle = C1/C2.

⇒  C1/C2  =  2πx/5πx.

⇒  C1/C2  = 5.

Therefore, the ratio of their circumference is 2/5.