Question

The circumference of the Chakra of the National flag exceeds its diameter by 16.8 cm. Find the radius of the chakra.

Answer 1

Hint: In this question, from the formula of circumference of a circle by assuming radius as r we need to equate it to the sum of diameter and 16.8. Now, on solving the formed equation we can get the value of the radius. Circumference of a circle is given by $C$\[=2\pi r\].

Complete step-by-step answer:
Circle is defined as the locus of a point which moves in a plane such that its distance from a fixed point in that plane is constant.
Let the radius of the circle is r and diameter is d.
Diameter of the circle is given by:
\[d=2r\]
Circumference of the circle is given by:
\[2\pi r\]
As we already know that the Chakra of the National flag is in the form of a circle.
Now, from the conditions given in the question by using the above formulae we can write it as:
\[\Rightarrow 2\pi r=d+16.8\]
Let us now substitute the value of d in terms of r in the above equation.
\[\Rightarrow 2\pi r=2r+16.8\]
Now, on writing the r times on the left hand side we get,
\[\Rightarrow 2\pi r-2r=16.8\]
Let us now take the common terms out.
\[\Rightarrow 2r\left( \pi -1 \right)=16.8\]
Now, on further simplification we get,
\[\Rightarrow 2r\left( 3.14-1 \right)=16.8\text{ }\left[ \because \pi =3.14 \right]\]
\[\Rightarrow 2r\times 2.14=16.8\]
\[\Rightarrow r\times 4.28=16.8\]
Let us now divide with 4.28 on both the sides then we get,
\[\begin{align}
  & \Rightarrow r=\dfrac{16.8}{4.28} \\
 & \therefore r=3.925 \\
\end{align}\]
Hence, the radius of the Chakra is 3.925 cm.

Note: Instead of writing the diameter in terms of radius we can also write the circumference in terms of the diameter and then on simplification we get the value of the diameter. Then by using the relation between the diameter and radius of a circle we can then get the value of radius. Both the methods give the same result.
While rearranging the terms and while doing the arithmetic operations we need to be careful about the terms because neglecting any of the changes the corresponding equation and so the value of the radius also changes.