NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.4

Question 13

Step 1: The diameters are in the ratio \(1:2:3\).

That means the radii are also in the ratio \(1:2:3\), because radius = diameter ÷ 2.

Step 2: The area of a circle depends on the square of its radius:

\( A = \pi r^2 \)

Step 3: Since the radii are in ratio \(1:2:3\), the areas of the full circles will be in the ratio:

\(1^2 : 2^2 : 3^2 = 1 : 4 : 9\).

Step 4: Now find the areas of each region (ring):

• Innermost circle area = \(1\) unit².
• Middle ring area = (area of radius 2 circle) − (area of radius 1 circle) = \(4 − 1 = 3\) unit².
• Outer ring area = (area of radius 3 circle) − (area of radius 2 circle) = \(9 − 4 = 5\) unit².

Step 5: So the ratio of the areas of the three regions is:

\(1 : 3 : 5\).

Final Answer: \(\boxed{1 : 3 : 5}\)