NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.1

Question 9

Step 1: Write the given data.

First circle has diameter = 36 cm = 0.36 m. Radius \(r_1 = \tfrac{0.36}{2} = 0.18\, \text{m}\).

Second circle has diameter = 20 cm = 0.20 m. Radius \(r_2 = \tfrac{0.20}{2} = 0.10\, \text{m}\).

Step 2: Find circumferences of the two circles.

Formula: Circumference of a circle = \(2 \pi r\).

So, \(C_1 = 2 \pi r_1 = 2 \pi (0.18) = 0.36 \pi\, \text{m}\).

\(C_2 = 2 \pi r_2 = 2 \pi (0.10) = 0.20 \pi\, \text{m}\).

Step 3: Add the two circumferences.

Total circumference = \(C_1 + C_2 = 0.36 \pi + 0.20 \pi = 0.56 \pi\, \text{m}\).

Step 4: Let the required circle have radius \(R\,\text{m}\). Then its circumference = \(2 \pi R\).

We are told this is equal to the total circumference: \(2 \pi R = 0.56 \pi\).

Step 5: Solve for \(R\).

Divide both sides by \(2\pi\): \(R = \tfrac{0.56}{2} = 0.28\, \text{m}\).

Step 6: Convert back into cm.

\(0.28\, \text{m} = 28\, \text{cm}\).

Final Answer: The radius of the required circle is 28 cm. So the correct option is (C) 28 cm.