MCQ
Numerical: Mensuration 2D — Circle MCQ - Practice Questions with Answers
Solve 15 Numerical: Mensuration 2D — Circle questions for RAS/RPSC preparation.
Practice questions
Q1The area of a circle is 154 cm². Using π = 22/7, identify the correct radius of the circle.
For a circle, area A = πr². The given area is 154 cm² and π = 22/7. So, 154 = (22/7) × r². Hence r² = 154 × 7 ÷ 22. Since 154 ÷ 22 = 7, r² = 7 × 7 = 49. Therefore r = √49 = 7. This value is the radius, not the diameter. The correct radius of the circle is 7 cm.
Q2For a circle of radius 7 cm, match the quantities with their correct values: 1. diameter, 2. circumference, 3. area, 4. area of the semicircle. Take π = 22/7.
For radius 7 cm, diameter = 2r = 14 cm. Circumference = 2πr = 2 × 22/7 × 7 = 44 cm. Area = πr² = 22/7 × 7 × 7 = 154 sq cm. A semicircle is half of the circle, so its area = 154 ÷ 2 = 77 sq cm. Thus the correct matching is 1-14 cm, 2-44 cm, 3-154 sq cm and 4-77 sq cm.
Q3A circular track has a diameter of 28 m. Using π = 22/7, what is its circumference?
For the circumference of a circle, use C = πd when the diameter is given. Here d = 28 m and π = 22/7. So, C = (22/7) × 28. Since 28 ÷ 7 = 4, the circumference is 22 × 4 = 88. No radius squaring is needed because the question asks for the boundary length. Therefore, the circular track has a circumference of 88 m.
Q4The circumference of a circle is 44 cm. Taking π = 22/7, find its area.
For a circle, circumference = 2πr. Here 44 = 2 × 22/7 × r, so 44 = 44r/7 and r = 7 cm. Now area = πr² = 22/7 × 7 × 7 = 22 × 7 = 154 sq cm. The given value 44 cm is only the circumference; after finding the radius, the area formula must be applied separately. Therefore, the area of the circle is 154 sq cm.
Q5The radius of a circle is increased from 7 cm to 14 cm. Taking π = 22/7, which of the following statements is incorrect?
Original radius = 7 cm. Original circumference = 2πr = 2 × 22/7 × 7 = 44 cm, and original area = 22/7 × 7 × 7 = 154 sq cm. New radius = 14 cm. New circumference = 2 × 22/7 × 14 = 88 cm, and new area = 22/7 × 14 × 14 = 616 sq cm. Increase in area = 616 − 154 = 462 sq cm. The circumference has become 88 ÷ 44 = 2 times, not 4 times. Hence statement D is incorrect.
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More questions
6For a circle of radius 21 cm, using π = 22/7, which statement is incorrect?
7Match List I with List II for circles, using π = 22/7. List I: P. radius 7 cm, Q. diameter 42 cm, R. circumference 88 cm, S. radius 21 cm. List II: 1. area 154 cm², 2. circumference 132 cm, 3. radius 14 cm, 4. area 1386 cm².
8Assertion: A circle with diameter 42 cm has an area of 1386 cm². Reason: The area of a circle is πr², and the radius is half of the diameter. Using π = 22/7, choose the correct option.
9A circular flower bed has radius 14 m. A path of uniform width 7 m is made around it. Taking π = 22/7, find the area of the path.
10The radius of a circular garden is 14 m. Using π = 22/7, find its area.
11Assertion: The circumference of a circle with radius 35 cm is 220 cm. Reason: Circumference of a circle is calculated by 2πr, and π = 22/7 is used here.
12A circle has diameter 28 cm. Using π = 22/7, which statement is correct?
13A sector of a circle has radius 21 cm and central angle 120°. Taking π = 22/7, which of the following statements is correct?
14Match the quantities for a circle of radius 7 cm using π = 22/7: 1. Circumference, 2. Area, 3. Area of semicircle, 4. Area of quadrant.
15The radius of a circular garden is 14 cm. Using π = 22/7, find its area.