A circle has the curious shape where all points on its outermost border have the same distance from the center. This center is commonly described by a point. On measuring the distance around the circle (circumference) and dividing it by the distance across the same circle, cutting right through the center (diameter), you’ll get an approximate value equivalent to 3.14159265358979323846… It goes on, but we’ll stick to the first few digits.

3.14 is mathematically adopted as the value for π (pronounced Pi). Using the above logic, you can understand how you get Pi by dividing the two factors mentioned earlier.

C/d=π

Even on something as a round plate, apply these measurements and you’ll prove the equation right. What’s the radius, then? It’s the distance from the circle’s center to any point on its circumference. It’s half a diameter, basically, or the diameter is twice the radius, whichever way you look at it.

d=2r

Linear units like inches and centimeters are what radii are measured by. A circle can have many diameters and radii, all passing through or sourcing from the center, respectively. You can see something like this in a bicycle wheel and the way its spokes are built.

Let’s delve into exercises and see all the ways you can use the above mentioned principles and equations to determine various things about circles. Keep in mind that π = 3.14

Exercise 1: The radius of a circle is 2 inches. What is the diameter?

Answer: Use the formula above. D = 2 x r

D = 2 x (2 inches)

Diameter = 4 inches. It’s that simple!

Exercise 2: The diameter of a circle is 3 centimeters. What is the circumference?

Answer: Don’t grow anxious seeing such shifts in demands. It’s alright to feel so, but get with the game. See what’s needed (circumference). See what you’re provided (Diameter). Use the appropriate equation (C = π x d) and you’re all set to get it right.

C = π x d

C = 3.14 x (3 cm)

C = 9.42 cm

Exercise 3: The radius of a circle is 2 inches. What is the circumference?

Answer: Once more, see what you’re asked (Circumference), what you’re provided (Radius), the equation to be used (C = π x d).

Let’s start by spotting the obvious. We don’t know ‘d’ or diameter. We do know its formula, though.

D = 2 x r

D = 2 x 2 = 4

D = 4 inches.

Now, with this at hand, let’s leap onto ‘C’.

C = π x d

C = 3.14 x 4 = 12.56

C = 12.56 inches. Voila!

Exercise 4: The circumference of a circle is 15.7 centimeters. What is the diameter?

Answer: Do the drill… Needed, Diameter. Provided, Circumference. Equation, C = π x d

C = π x d

15.7 cm = 3.14 x d

Now, this is rather curious. It’s all twisted! This is how you untangle them. Isolate the unknown ‘d’ and when that happens, his partner leaves him for the other side, thereby dividing their marriage. Memorable analogy, huh?

15.7 / 3.14 = d (or) d = 15.7 / 3.14

D = 5 cm.

That’s all there is to the basics of Circumference, Diameter and Radius of a Circle.

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