NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.3

Question 6

Step 1: Identify the shape

The figure looks like a rectangle in the middle with two semicircles (half-circles) attached at the two ends. Together, the two semicircles make one complete circle.

Step 2: Note the given measurements

• Overall length = 38 cm
• Overall width (also the diameter of semicircle) = 10 cm

Step 3: Find the radius of the semicircle

Radius = Diameter ÷ 2 = 10 ÷ 2 = 5 cm.

Step 4: Find the length of the rectangular part

The full length = 38 cm. But at both ends we have semicircles of radius 5 cm each, so total semicircle length = 2 × 5 = 10 cm. Rectangular part length = 38 – 10 = 28 cm.

Step 5: Calculate the area of the rectangle

Area = Length × Breadth = 28 × 10 = 280 cm².

Step 6: Calculate the area of the circle formed by the two semicircles

Area of circle = πr² = π × 5² = 25π cm².

Step 7: Add both areas

Total Area = Rectangle area + Circle area = 280 + 25π cm².

Step 8: Approximate value

If we take π ≈ 3.14, 25π ≈ 25 × 3.14 = 78.5. So total area ≈ 280 + 78.5 = 358.5 cm².

Final Answer: 280 + 25π cm² (≈ 358.5 cm²)