Numerical: Mensuration 2D — Circle MCQ — 15 Practice Questions with Answers

Explanation

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.

Explanation

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.

Explanation

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.

Explanation

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.

Explanation

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.