Diameter Formula
Diameter is defined as the line passing through the center of a circle having two extremes on the circumference of a circle.
The Diameter of a circle divided the circle into two equal parts known as semi-circle.
The center of a circle is the midpoint of its diameter. It divides the diameter into two equal parts, each of which is a radius of the circle. The radius is half the diameter.
We all know that A chord of a circle is a straight line segment whose endpoints both lie on the circle. Thus it can be said that the diameter is the longest possible chord on any circle.
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Relation between Radius and Diameter:
We know that the the distance from the center point to any point on the circumference of a circle is a fixed distance, known as the Radius of a circle.
Therefore, the relation between Radius and Diameter is
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Formula for Area and circumference in Terms of Diameter:
Circumference:
We know
Circumference =
It can be re-written as,
=
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Area:
We know
Area= Â
It can be re-written as
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Let’s Work Out- Example: Find the diameter of the circle whose radius is 8 cm ? Also find the Area of a circle. Solution: Given, Radius of the circle (r) = 8 cm Diameter of the circle = 2r = = 16 cm Now Area \(\begin{array}{l}\frac{\pi }{4}.d^{2}\end{array} \)
\(\begin{array}{l}\frac{\pi }{4}.16^{2}\end{array} \)
= 200.96 cm2 Â Example: Find the diameter of the circle whose Area is 154cm2? Also, find the circumference of the circle. (Take Solution: Given, Area of the circle (A) = 154cm2 We know Area (A) =Â
\(\begin{array}{l}\Rightarrow 154=\frac{22}{7.4}.d^{2}\end{array} \)
\(\begin{array}{l}\Rightarrow d^{2}=7^{2}.4=7^{2}.2^{2}\end{array} \)
 Now Finding the Circumference of a circle which is equal to, \(\begin{array}{l}C=\pi d\end{array} \)
\(\begin{array}{l}=\frac{22}{7} \times 14 \end{array} \)
= 44 cm |
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