Mensuration of 2D Shapes - Exam Prep for Competitive Exams

Mensuration of 2D Shapes - Problems on Circles - Applications

Q. A circle is inscribed in a square with a side length of 10 cm. What is the area of the circle?

A. 78.5 cm²
B. 100 cm²
C. 50 cm²
D. 25 cm²

Solution

Radius of the circle = side length / 2 = 10 / 2 = 5 cm. Area = πr² = π(5)² = 25π ≈ 78.5 cm².

Correct Answer: A — 78.5 cm²

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Q. A circle is inscribed in a square with a side length of 8 cm. What is the area of the circle?

A. 50.24 cm²
B. 64 cm²
C. 25.12 cm²
D. 32 cm²

Solution

Radius = side length / 2 = 8 / 2 = 4 cm. Area = πr² = π(4)² = 16π ≈ 50.24 cm².

Correct Answer: A — 50.24 cm²

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Q. A sector of a circle has a radius of 5 cm and a central angle of 60 degrees. What is the area of the sector?

A. 13.09 cm²
B. 25 cm²
C. 15.71 cm²
D. 20.94 cm²

Solution

Area of sector = (θ/360) * πr² = (60/360) * π(5)² = (1/6) * 25π ≈ 13.09 cm².

Correct Answer: A — 13.09 cm²

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

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

Solution

Area of sector = (θ/360) * πr² = (60/360) * π(6)² = (1/6) * 36π = 6π cm².

Correct Answer: B — 6π cm²

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Q. If a circle has an area of 50 cm², what is its radius?

A. 5 cm
B. 7.07 cm
C. 10 cm
D. 8 cm

Solution

Area = πr², so r = √(Area/π) = √(50/π) ≈ 7.07 cm.

Correct Answer: B — 7.07 cm

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Q. If a circle has an area of 78.5 cm², what is its radius?

A. 5 cm
B. 7 cm
C. 10 cm
D. 6 cm

Solution

Area = πr², so r = √(Area/π) = √(78.5/π) ≈ 5 cm.

Correct Answer: B — 7 cm

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Q. If the diameter of a circle is 12 cm, what is its area?

A. 113.04 cm²
B. 36 cm²
C. 144 cm²
D. 28.26 cm²

Solution

Radius = diameter / 2 = 12 / 2 = 6 cm. Area = πr² = π(6)² = 36π ≈ 113.04 cm².

Correct Answer: A — 113.04 cm²

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Q. What is the diameter of a circle with a circumference of 62.8 cm?

A. 20 cm
B. 10 cm
C. 15 cm
D. 5 cm

Solution

Diameter = Circumference / π = 62.8 / π ≈ 20 cm.

Correct Answer: A — 20 cm

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Q. What is the length of the arc of a circle with a radius of 4 cm and a central angle of 90 degrees?

A. 3.14 cm
B. 6.28 cm
C. 12.56 cm
D. 1.57 cm

Solution

Arc length = (θ/360) * 2πr = (90/360) * 2π(4) = (1/4) * 8π = 2π ≈ 6.28 cm.

Correct Answer: A — 3.14 cm

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Q. What is the perimeter of a circle with a radius of 10 cm?

A. 31.4 cm
B. 62.8 cm
C. 20 cm
D. 15.7 cm

Solution

Perimeter (Circumference) = 2πr = 2π(10) = 20π ≈ 62.8 cm.

Correct Answer: B — 62.8 cm

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Q. What is the perimeter of a circle with a radius of 3 cm?

A. 18.84 cm
B. 9.42 cm
C. 12.56 cm
D. 6.28 cm

Solution

Perimeter (Circumference) = 2πr = 2π(3) = 6π ≈ 18.84 cm.

Correct Answer: A — 18.84 cm

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Q. What is the perimeter of a semicircle with a diameter of 14 cm?

A. 21 cm
B. 28 cm
C. 22 cm
D. 35 cm

Solution

Perimeter = diameter + arc length = 14 + (π * radius) = 14 + (π * 7) ≈ 14 + 21.99 ≈ 35 cm.

Correct Answer: C — 22 cm

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Mensuration of 2D Shapes - Problems on Circles - Applications

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