Exercise 6.3

Find the area of a sector of a circle with radius 7 cm if the angle of the sector is 60°.

Find the area of a quadrant of a circle whose circumference is 44 cm.

The length of the minute hand of a clock is 7 cm. Find the area swept by the minute hand in 10 minutes.

A chord of a circle of radius 10 cm subtends 90° at the centre. Find the area of the corresponding: (i) minor sector (that subtends 90° at the centre) and (ii) major sector (that subtends 270° at the centre) (Use π = 3.14)

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre of the circle. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)

A car has two wipers which do not overlap. Each wiper has a blade of length 28 cm and sweeps through an angle of 120°. Find the total area cleaned at each swipe of the blade.

A chord of a circle of radius \(r\) subtends an angle of 60° at the centre of the circle. Show that the area of the corresponding minor segment of the circle is equal to π\(r^2(\frac{1}{6} − \frac{√3}{4})\).

An equilateral triangle is inscribed in a circle of radius \(r\). Show that the ratio of the area of the triangle to the area of the circle is equal to \(\frac{3√3}{4π} ≈ 0.413

A square is inscribed in a circle of radius \(r\). Show that the ratio of the area of the square to the area of the circle is equal to \(\frac{2}{π}\) ≈ 0.637.

A hexagon is inscribed in a circle of radius \(r\). Show that the ratio of the area of the circle is equal to \(\frac{3√3}{2π}\) ≈ 0.827. Can you see why the answer is exactly twice the answer to Question 8?