Areas Related to Circles — Important Questions
Gujarat Board · Class 10 · Mathematics
45 important questions from Areas Related to Circles for Gujarat Board Class 10 Mathematics, with answers. Written for the board exams 2027.
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Important Questions from Areas Related to Circles
Which of the following are correct formulas? (Select all that apply)
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Area of sector = (θ/360°) × πr², Arc length = (θ/360°) × 2πr, Area of segment = Area of sector - Area of triangle
The correct formulas are: Area of sector = (θ/360°) × πr², Arc length = (θ/360°) × 2πr, and Area of segment = Area of sector - Area of triangle. The area of circle is πr², not 2πr².
A circular field has radius 21 m. Find the area of a sector with central angle 120°.
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462 m²
Area of sector = (120°/360°) × π × 21² = (1/3) × π × 441 = 147π = 462 m²
The radius of a circle is doubled. How does this affect the area of a sector with the same central angle?
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Area becomes 4 times
Since Area ∝ r², when radius is doubled (r becomes 2r), the area becomes (2r)² = 4r², which is 4 times the original area.
Find the perimeter of a sector with radius 10 cm and central angle 72°.
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32.57 cm
Perimeter of sector = Arc length + 2 × radius = (72/360) × 2π × 10 + 2 × 10 = (1/5) × 20π + 20 = 4π + 20 = 12.57 + 20 = 32.57 cm
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