Question

What is the circumference of a circle with Diameter of 28 inches?

Answer 1

Hint: We are given the diameter of the circle and we have to find the circumference of this circle. Now, diameter is the distance between two points on a circle passing through the center. Hence, the diameter of the circle is 2 times its radius. Using this formula, we can find the radius of the given circle. Now, the circumference of circle is given by the formula
 $ \to Circumference = 2\pi r $

Complete step-by-step answer:
In this question, we are given a circle and its diameter. We have to find its circumference.
 $ \to D = 28 $ inches.
 $ \to r = $ ?
 $ \to Circumference = $ ?
Now, first of all let us understand what circle, diameter and radius are.
So, a circle is the collection of all the points lying in a plane at a given distance from the center point.
The distance between the center and all the points on the circle is known as radius.
The distance between two points on the circle passing from the center is known as the diameter of the circle.
Now, the diameter is double in length as compared to the radius.
So, we can say that the diameter of circle is equal to 2 times its radius.
  $ \to d = 2r $
Now, we have the diameter as 28 inches and we have to find the radius. Therefore,
 $ \to 2r = 28 $
Divide both sides by 2, we get
 $ \to r = \dfrac{{28}}{2} $
 $ \to r = 14 $ inches
Hence, the radius of the circle having diameter 28inches is 14inches.
Now, circumference of a circle is given by the formula
 $ \to Circumference = 2\pi r = 2 \times 3.14 \times 14 = 87.92 $ inches
Hence, the circumference of the circle whose diameter is 28 inches is 87.92 inches.
So, the correct answer is “ 87.92 inches.”.

Note: To find the area of the circle, we can use the given two formulas.
When diameter is given:
 $ \to Area = \pi \times \dfrac{{{d^2}}}{4} $
For example: $ d = 2 $
 $ \to Area = 3.14 \times \dfrac{{{2^2}}}{4} = 3.14 $
When radius is given:
 $ \to Area = \pi \times {r^2} $
For example: $ r = 4 $
 $ \to Area = 3.14 \times {4^2} = 50.24 $