Circumference to Diameter
Introduction to convert circumference to diameter
If we put a bangle or a one – rupee coin on the plane of the paper and move pencil around it, we obtain a closed curve shown below.
Such a closed curve is called a circle.
A circle is a simple closed curve all of whose points are at same distance from a fixed point inside it. A line segment which passes through the centre of the circle and whose end points lie on the circle, is called a diameter of the circle.
The perimeter of a circle is called its circumference. We can measure the circumference of a circle by using a piece of thread. Mark a point A on the circle. Keep one end of the thread at A. spread the thread along the boundary of the circle. Mark the point on the thread which again falls on A. measure the length of the thread up to this point.
This gives the circumference of the circle.
If we draw several circles and measures the circumference and diameter of each, we shall find find each case that
$\frac{circumference}{diameter}$ = 3.14 or $\frac{22}{7}$
We denote $\frac{22}{7}$ or 3.14 by the symbol pie.
Thus,
Circumference of a circle = $\pi$ x diameter of the circle
= 2$\pi$ x radius of the circle.
Therefore, 2 x $\pi$ x radius
And, Radius = circumference/ 2$\pi$
Diameter = circumference/$\pi$
Ex:1 Find the diameter of a circle whose circumference is 31.4cm. [ take ∏ =3.14]
Sol: Given,
Circumference of circle = 31.4
Pi x diameter = 31.4
Diameter of circle = $\frac{31.4}{3.14}$
Hence, diameter of circle = 10 cm
Ex:2 Find the diameter of a circle whose circumference is 44 cm.[take ∏ = $\frac{22}{7}$]
Sol: circumference of the circle = 44 cm
Diameter of circle = circumference/ $\pi$
= $\frac{44}{22/7}$
= $\frac{44 x 7}{22}$
= 14 cm
Hence, the diameter of circle = 14 cm
Ex 3: Find the diameter of the circle when the circumference of the circle is 25 cm
Sol:
Let the diameter of the circle is d cm
Circumference of the circle is pi*d units
25 = pi*d
(25/3.14) = d
7.96 =d
The diameter of the circle is 7.9cm.
Ex 4: Find the diameter of the circle when the circumference of the circle is 36 cm
Sol:
Let the diameter of the circle is d cm
Circumference of the circle is pi*d units
36 = pi*d
(36/3.14) = d
11.5 =d
The diameter of the circle is 11.5cm.
Ex 1: Find the circumference of the circle when the diameter is 10 cm
Sol:
Diameter of the circle is 10cm
Circumference of the circle is pi*d units
= (3.14)*10
= 31.4 cm.
Circumference of the circle is 31.4 cm
Ex 2.Find the circumference of the circle when the diameter is 8cm
Sol:
Diameter of the circle is 8cm
Circumference of the circle is pi*d units
= (3.14)*8
= 25.12 cm
Circumference of the circle is 25.12cm
Ex: 3 Find the circumference of a circle whose radius is 3.5 cm. [ take ∏ = $\frac{22}{7}$]
Sol: Radius of the circle = 3.5 cm = $\frac{7}{2}$
Therefore, circumference of the circle = 2 x $\pi$ x Radius of the circle
= 2 x $\frac{22}{7}$ x $\frac{7}{2}$
= 22 cm
Practice problem:
1. Find the circumference of the circle when the diameter is 20 cm
Ans is 62.8 cm
2. Find the diameter of the circle when the circumference of the circle is 97.2 cm
Ans is 30.9 cm
