# NCERT Class 9 Mathematics Chapter 6 Measuring Space: Perimeter and Area Solutions: In-Text and Exercise Questions Explained | SwaVid

Here are the real questions from NCERT Class 9 Mathematics textbook "Ganita Manjari", "Measuring Space: Perimeter and Area" (SwaVid public chapter 6), a...

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# Measuring Space: Perimeter and Area

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Chapter 6 · Class 9 Mathematics

Here are the real questions from NCERT Class 9 Mathematics textbook "Ganita Manjari", "Measuring Space: Perimeter and Area" (SwaVid public chapter 6), along with step-by-step worked solutions. Please note that the provided PDF link in the prompt was for a different chapter; the questions and solutions below are based on the correct Chapter 6 of "Ganita Manjari" as identified through Google Search.

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In-text Questions

Answer: (8/3)πr units

The figure 6.12 shows two circles intersecting, and the perimeter refers to the outer boundary of the combined shape.

Exercise Set 6.1

Exercise Set 6.2

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- When two circles of equal radius 'r' pass through each other's centers, the distance between their centers is 'r'.
- The points of intersection and the two centers form two equilateral triangles. For example, if the centers are C1 and C2, and intersection points are A and B, then C1AC2 and C1BC2 are equilateral triangles with side length 'r'.
- Consider one circle. The common chord (AB) subtends an angle of 120° at the center of each circle (since each equilateral triangle contributes 60° to the angle formed by the radii to the intersection points, so 60° + 60° = 120°).
- The perimeter of the combined shape is formed by two major arcs, one from each circle. Each major arc corresponds to the angle (360° - 120°) = 240°.
- The length of one such arc is given by the formula L = (θ/360°) × 2πr, where θ = 240°.
- L = (240/360) × 2πr = (2/3) × 2πr = (4/3)πr.
- Since the shape's perimeter consists of two such identical arcs, the total perimeter is 2 × (4/3)πr.
- NCERT Class 9 Mathematics textbook: Ganita Manjari : Chapter 6: Measuring Space: Perimeter and Area

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