What about a circle? What is its perimeter (usually called the circumference) in terms of its diameter? Class 9

What about a circle? What is its perimeter (usually called the circumference) in terms of its diameter? Class 9

Question 1.

What about a circle? What is its perimeter (usually called the circumference) in terms of its diameter? Is the ratio of circumference (C) to diameter (D) the same for circles of all sizes? What do you think? Class 9

Answer:

All circles are similar figures. This means that if a circle is enlarged or reduced, all its lengths change in the same proportion.

So, when the diameter of a circle changes, its circumference also changes in the same ratio. Hence, the ratio $\frac{C}{D}$ remains constant for all circles.

This constant ratio is called π(pi).

Question 1.

The circumference of a circle of diameter d is given by πd.

Since the diameter is twice the radius, it can also be written as 2πr, where r is the radius. Class 9

Based on this, what will be the length of a semicircle having the same radius r.

Answer:

The circumference of a full circle = 2πr

semicircle is half of a circle, so its length (arc length) will be = $\frac{1}{2}$ × 2πr = πr