Question

Draw concentric circles for radii measuring 4.2 cm and 6.8 cm. Find out the width of circular ring.

Answer 1

Hint: In the solution, draw a circle of radius 4.2 cm, mark the centre of the circle for this, then take a radius of 6.8 cm and use the existing centre of the circle to draw this circle. Now, we can say that both circles are concentric and can find the width of the circular ring easily.

Complete step-by-step answer:
Given
The radius of the first circle or small circle is \[r = 4.2\,{\rm{cm}}\]
The radius of the second circle or large circle is\[R = 6.8\,{\rm{cm}}\].

Using the given radius of two circles, firstly draw the small circle of radius 4.2 cm and mark the centre of the circle as O, then draw the bigger circle or second circle of radius 6.8 cm using the marked centre point of the first circle.
Now we can see that the two circles are one above the other, we call them concentric circles.
The equation to find the width of the circular ring will be,
We can find the width of the circular ring by subtracting the smaller radius from the bigger circle radius.
\[w = R - r\]
Here, w will be the width of the circular ring.
Substituting the values in the above equation, then we will get
\[
w = R - r\\
= 6.8\,{\rm{cm}} - 4.2\,{\rm{cm}}\\
{\rm{ = }}2.6\,{\rm{cm}}
\]
Therefore, the width of the circular ring is 2.6 cm.

Note: In the question, it is given that to find the width of the circular ring, we may be confused by the term width in the circle concept, but we should understand it as the distance or gap between the bigger or second circle and the smaller or first circle.