Mensuration of 2D Shapes - Exam Prep for Competitive Exams

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Mensuration of 2D Shapes - Problems on Circles - Case Studies

Q. A circle has a radius of 3 cm. What is the length of its diameter?

A. 3 cm
B. 6 cm
C. 9 cm
D. 12 cm

Solution

Diameter = 2 * radius = 2 * 3 cm = 6 cm.

Correct Answer: B — 6 cm

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Q. A circle has an area of 78.5 cm². What is its radius?

A. 5 cm
B. 7 cm
C. 10 cm
D. 8 cm

Solution

Area = πr², so r² = Area/π = 78.5/π ≈ 25, thus r ≈ 5 cm.

Correct Answer: B — 7 cm

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Q. What is the area of a sector with a radius of 6 cm and a central angle of 120 degrees?

A. 12π cm²
B. 18π cm²
C. 8π cm²
D. 10π cm²

Solution

Area of sector = (θ/360) * πr² = (120/360) * π(6)² = (1/3) * 36π = 12π cm².

Correct Answer: A — 12π cm²

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Q. What is the area of a sector with a radius of 6 cm and a central angle of 60 degrees?

A. 12π cm²
B. 6π cm²
C. 3π cm²
D. 9π cm²

Solution

Area of sector = (θ/360) * πr² = (60/360) * π(6)² = 12π cm².

Correct Answer: A — 12π cm²

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Q. What is the distance between the points (2, 3) and (5, 7) in a coordinate plane?

A. 5
B. 4
C. 3
D. 6

Solution

Distance = √((x2 - x1)² + (y2 - y1)²) = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

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Q. What is the perimeter of a semicircle with a diameter of 10 cm?

A. 15.7 cm
B. 20 cm
C. 25 cm
D. 30 cm

Solution

Perimeter = diameter + arc length = 10 + (π * radius) = 10 + (π * 5) ≈ 10 + 15.7 = 25.7 cm.

Correct Answer: A — 15.7 cm

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Q. What is the perimeter of a semicircle with a diameter of 12 cm?

A. 18.84 cm
B. 12 cm
C. 24 cm
D. 36 cm

Solution

Perimeter = (π * r) + diameter = (π * 6) + 12 ≈ 18.84 cm.

Correct Answer: A — 18.84 cm

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