1. The area of a circle with radius 'r' is:
Answer:
Explanation:
The formula to calculate the area of a circle is π times the square of its radius.
2. If the circumference of a circle is 44 cm, then its radius is:
Answer:
Explanation:
Circumference = 2πr. If circumference is 44 cm, then 2πr = 44, which gives r = 7 cm.
3. The area of a sector of angle 120° in a circle of radius 14 cm is:
Answer:
Explanation:
Area of sector = (θ/360) x πr^2 = (120/360) x 22/7 x 14 x 14 = 184 cm^2.
4. The length of an arc of a sector with a radius of 7 cm and central angle of 60° is:
Answer:
Explanation:
Length of an arc = (θ/360) x 2πr = (60/360) x 2π x 7 = 11π/3 cm.
5. The perimeter of a semi-circle of radius 7 cm is:
Answer:
Explanation:
Perimeter includes the curved part (πr) and the diameter (2r). For a semi-circle, it's πr + 2r.
6. The area enclosed between two concentric circles is called:
Answer:
Explanation:
The region between two concentric circles is termed as annulus.
7. A circular park has a path 7m wide running inside it along its boundary. If the area of the path is 462 m^2, then the radius of the park is:
Answer:
Explanation:
Let the radius be r. The area of the path = π(r^2 – (r-7)^2) = 462 m^2. Solving gives r = 28 m.
8. The area of the largest triangle that can be inscribed in a semi-circle of radius 'r' is:
Answer:
Explanation:
The largest triangle inscribed in a semi-circle is a right triangle with the hypotenuse as the diameter. The area is ½ x base x height = ½ r^2.
9. The area of a circular ring is 616 cm^2. If the outer radius is 14 cm, the inner radius is:
Answer:
Explanation:
Area of ring = π(14^2 – r^2) = 616 cm^2. Solving gives inner radius r = 6 cm.
10. A quarter circle of radius 14 cm is cut out from a square paper of side 14 cm. The area of the remaining paper is:
Answer:
Explanation:
Remaining area = Area of square – Area of quarter circle = 14^2 – ¼π(14^2) = 196 – 49π cm^2.