Advertisements
Advertisements
प्रश्न
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of the segment formed by the corresponding chord. (Use π = `22/7`)
उत्तर
Area of the segment APB = [Area of the sector AOB] − [Area of ΔAOB] ....(1)
In AOB, OA = OB = 21 cm
∴ ∠A = ∠B = 60° ...(∴ ∠O = 60°)
AOB is an equilateral triangle.
∴ AB = 21 cm
∴ Area of ΔAOB = `sqrt3/4` (side)2 ....[∴ ΔAOB is an equilateral triangle]
`= sqrt3/4 xx 21 xx 21 "cm"^2`
= `(441sqrt3)/4` cm2 ...(2)
Using part (ii) and (2) in (1), we have
Area of the segment = `[231 "cm"^2] − [(441sqrt3)/4 "cm"^2]`
`= (231 - (441sqrt3)/4) "cm"^2`
संबंधित प्रश्न
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60° [Use `pi = 22/7`]
In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.
A sector of 56° cut out from a circle contains area of 4.4 cm2. Find the radius of the circle
A chord 10 cm long is drawn in a circle whose radius is 5√2 cm. Find the area of both
segments
In the given figure, A is the center of the circle. ∠ABC = 45° and AC = 7√2 cm. Find the area of segment BXC.
In the given figure, O is the centre of the circle. m ( arc PQR) = 60° OP = 10 cm. Find the area of the shaded region.( \[\pi\]= 3.14, \[\sqrt{3}\]= 1.73)
Choose the correct alternative answer for the following question.
Find the perimeter of a sector of a circle if its measure is 90° and radius is 7 cm.
A chord of length 6 cm is at a distance of 7.2 cm from the centre of a circle. Another chord of the same circle is of length 14.4 cm. Find its distance from the centre.
In following fig., PT is a tangent to the circle at T and PAB is a secant to the same circle. If PA = 4cm and AB = Scm, find PT.
A car has two wipers that do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Find the total area cleaned at each sweep of the blades. `("Take" π =22/7)`
If `theta` is the angle in degrees of a sector of a circle of radius V, then area of the sector is ____________.
The area of the sector of a circle with radius 6 cm and of angle 60° is ____________.
Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°.
A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle.
In figure, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region.
Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.
In figure, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region of the figure.
Floor of a room is of dimensions 5 m × 4 m and it is covered with circular tiles of diameters 50 cm each as shown in figure. Find the area of floor that remains uncovered with tiles. (Use π = 3.14)
The number of revolutions made by a circular wheel of radius 0.25 m in rolling a distance of 11 km is ______.
