A horse is tied to a pole fixed at one corner of a 30 m Ă 30 m square field ofgrass, by means of a 10 m long rope (figure). [Take Ď = 3.14.] (i) Find the area of that part of the field in which the horse can graze. (ii) Find the increase in the grazing area if the rope were 20 m long insteadof being 10 m long.
The circumference of a circle exceeds the diameter by 16.8 cm. Find the radius of the circle.
Find the area of the sector of a circle whose radius is 14 cm and angle of sector is 45°.
A pendulum swings through an angle of 30° and describes an arc 6.6 cm in length. Find the length of the pendulum. (Use π= 22/7)
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
A steel wire is in the form of a square encloses an area of 121 cm2. If the same wire is bent in the form of a circle, find the area of the circle.
Find the area of the segment of a circle, given that the angle of the sector is 120° and the radius of the circle is 21 cm. (use π=22/7)
Two circles touch internally. The sum of their areas is 116π cm2 and distance between their centres is 6 cm. Find the radii of the circles.
The area of the square that can be inscribed in a circle of radius 8 cm is
The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
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.
Find the area of the flower bed (with semi-circular ends) shown in figure.
Find the area of the shaded region in figure.
Find the area of the shaded region in figure, where arcs drawn with centers A, B, C and D intersect in pairs at mid-point P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. (Use π = 3.14)
A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then find the area of the road.
The area of a circular playground is 22176 m2. Find the cost of fencing this ground at the rate of Rs 50 per m.
The diameter of front and rear wheels of a tractor are 80 cm and 2m, respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.
Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60°. (Use π = 3.14)
Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.
On a square cardboard sheet of area 784 cm2, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
The central angles of two sectors of radii 7 cm and 21 cm are respectively 120° and 40°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?
Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.
In the given figure the boundary of the shaded region consists of four semi-circular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find
i) length of the boundary ii) Area of the shaded region
Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of 90° at the center.
Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of 176 m.
Fig., shows a sector of a circle, centre O, containing an angle θ°. Prove that:
(i)Perimeter of the shaded region is
(ii)Area of the shaded region is
