Exercise 11.1: Perimeter and Area of a Circle

If the length of an arc of a sector of a circle with radius 'r' is 'l', then which of the following expressions represents the area of the sector?

If the radius of a sector remains constant, but its central angle is doubled, then its area will ________.

If the radius of a sector is increased by 25% and its central angle is decreased by 20%, what is the percentage change in its area?

Ravi wants to find the length of the arc of a sector with radius 7 cm and angle 90°. He applies the formula: Arc Length = (90/360) × π(7)². What mistake did Ravi make?

A square ABCD has a side length of 7 cm. A quadrant of a circle with center A and radius AD is drawn inside the square. What is the area of the shaded region, which is the part of the square *outside* the quadrant? (Use π = 22/7)

In a square ABCD of side 14 cm, four equal circles are drawn such that each circle touches two other circles and two sides of the square. Find the area of the shaded region (the region of the square not covered by the circles). (Use π = 22/7)

From each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut from the centre. Find the area of the remaining portion of the square. (Use π = 22/7)

For a sector of a circle with radius 'r' and arc length 'L', which of the following expressions correctly represents its area 'A'?

A clock's minute hand is 10 cm long. How far does the tip of the minute hand move in 30 minutes? (Use π = 3.14)

Two circles touch externally. The sum of their areas is 130π cm² and the distance between their centres is 14 cm. Find the radii of the two circles.