Advertisements
Advertisements
प्रश्न
A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m × 16 m. Find the area of the field in which the cow can graze.
उत्तर
Let ABCD be a rectangular field.
Length of field = 20 m
Breadth of the field = 16 m
According to the question,
A cow is tied at a point A.
Let length of rope be AE = 14 m = l.
Angle subtended at the center of the sector = 90°
Angle subtended at the center (in radians) θ = `(90π)/180 = π/2`
∴ Area of a sector of a circle = `1/2 "r"^2θ`
= `1/2 xx (14)^2 xx (π/2)`
= 154 m2
Hence, the required area of a sector of a circle is 154 m2.
संबंधित प्रश्न
The perimeter of a sector of circle of radius 5.7m is 27.2 m. Find the area of sector.
The diagram shows a sector of circle of radius ‘r’ can containing an angle 𝜃. The area of sector is A cm2 and perimeter of sector is 50 cm. Prove that
(i) 𝜃 =`360/pi(25/r− 1)`
(ii) A = 25r – r2
In the given figure, if A is the centre of the circle. \[\angle\] PAR = 30°, AP = 7.5, find the area of the segment PQR. (\[\pi\] = 3.14)
The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6 : 05 am and 6 : 40 am.
Prove that the circle drawn with any side of a rhombus as a diameter, passes through the point of intersection of its diagonals.
Find the area of the sector of a circle of radius 8 cm and arc with length 15 cm.
In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?
In the given figure, arcs have been drawn of radius 7 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.
Find the area of the sector of a circle of radius 7 cm and of central angle 90°. Also, find the area of corresponding major sector.
What is the length of arc of a circle of radius 7 cm which subtends an angle of 90° at the centre of the circle?
