Mensuration of 2D Shapes - Exam Prep for Competitive Exams

Mensuration of 2D Shapes - Problems on Circles

Q. A circle has a diameter of 10 cm. What is its area?

A. 78.5 cm²
B. 31.4 cm²
C. 50 cm²
D. 100 cm²

Solution

Radius = diameter / 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 has a radius of 2.5 m. What is its circumference?

A. 15.7 m
B. 10 m
C. 5 m
D. 20 m

Solution

Circumference = 2πr = 2π(2.5) = 5π ≈ 15.7 m.

Correct Answer: A — 15.7 m

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Q. A circle has an area of 50.24 cm². What is its diameter?

A. 8 cm
B. 10 cm
C. 12 cm
D. 14 cm

Solution

Area = πr², so r = √(Area/π) = √(50.24/π) ≈ 4 cm. Diameter = 2r = 8 cm.

Correct Answer: B — 10 cm

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Q. A circle is inscribed in a square with a side length of 6 cm. What is the area of the circle?

A. 28.26 cm²
B. 36 cm²
C. 18.84 cm²
D. 12 cm²

Solution

Radius = side length / 2 = 6 / 2 = 3 cm. Area = πr² = π(3)² = 9π ≈ 28.26 cm².

Correct Answer: A — 28.26 cm²

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Q. If a circle has a radius of 3 cm, what is its diameter?

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

Solution

Diameter = 2 × radius = 2 × 3 = 6 cm.

Correct Answer: B — 6 cm

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Q. If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 90 degrees?

A. 2.36 cm
B. 3.14 cm
C. 4.71 cm
D. 7.07 cm

Solution

Arc length = (θ/360) * 2πr = (90/360) * 2π(3) = (1/4) * 6π = 4.71 cm.

Correct Answer: A — 2.36 cm

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Q. If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 60 degrees?

A. 3.14 cm
B. 3.77 cm
C. 5.24 cm
D. 6.28 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2π(3) = (1/6) * 6π = π ≈ 3.14 cm.

Correct Answer: B — 3.77 cm

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

A. 100 cm²
B. 200 cm²
C. 300 cm²
D. 400 cm²

Solution

Circumference = 2πr, so r = 62.8 / (2π) ≈ 10 cm. Area = πr² = π(10)² = 100π ≈ 314.16 cm².

Correct Answer: A — 100 cm²

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Q. What is the circumference of a circle with a radius of 4 cm?

A. 12.56 cm
B. 25.12 cm
C. 16 cm
D. 50.24 cm

Solution

Circumference = 2πr = 2π(4) = 8π ≈ 25.12 cm.

Correct Answer: A — 12.56 cm

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Q. What is the radius of a circle if its area is 50.24 cm²?

A. 4 cm
B. 5 cm
C. 6 cm
D. 7 cm

Solution

Area = πr², so r = √(Area/π) = √(50.24/π) ≈ 5 cm.

Correct Answer: B — 5 cm

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Q. What is the radius of a circle whose area is 113.04 cm²?

A. 6 cm
B. 7 cm
C. 8 cm
D. 9 cm

Solution

Area = πr², so r = √(Area/π) = √(113.04/π) ≈ 6 cm.

Correct Answer: B — 7 cm

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Mensuration of 2D Shapes - Problems on Circles

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