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Find the area of the shaded region where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre
Area of the shaded region
= Area of major sector of the cirlce + Area of equilateral triangle OAB
= ( – Area of minor sector)
Four horses are tethered at four corners of a square plot of 42 m so that they just cannot reach one another. The area left ungrazed is
Ungrazed area = Area of square – 4 (area of quadrants)
If the circumference of a circle is increased by 50%, by what percent will its area be increased?
Circumference
Increased circumference
Area
New area
Increased area
Percentage increase
The circumference of two circles are in the ratio 2:3. The ratio of their areas are
Ratio of areas
A Park is in the form of a rectangle \(120\ m\times100\ m \). At the centre of the park there is a circular lawn. The area of park excluding lawn is \(8700\ m^2 \). The radius of the lawn is
Area of park
Area of lawn
A/Q
The area enclosed between the concentric circle is \(770\ cm^2 \). If the radius of the outer circle is \(21\ cm \). The radius of the inner circle is
An archery tangent has 3 regions formed by three concentric circles. If the diameter of the concentric circles are in the ratio 1:2:3, the ratio of the areas of three regions is
Let the diameter of the centre circle = x
Radius
Area
Let the diameter of the middle circle be
Area
Area of region
Diameter of an outer circle
Area of region
Ratio
A square of diagonal 8 cm is inscribed in a circle. Find the area of the region lying inside the circle and outside the square.
Radius of the circle
Area of the region = Area of circle – Area of square
A path of 4 cm width runs round a semicircular grassy plot whose circumference is \(163\dfrac{3}{7}\ m \). The area of the path is
Area of path
A plot is in the form of a rectangle ABCD having semicircle on BC. If AB = 60 m and BC = 28 m. The area of the plot is
Area of plot = Area of rectangle + area of semicircle
A rectangular piece is 20 m long and 15 m wide. From its four corners, quadrants of radii 3.5 m have been cut. The area of the remaining part is
Area of rectangle
Area of 4 quadrants
Area of remaining part
In the figure, if AB=13 cm and AC=12 cm. Find the area of shaded region
Area of shaded region = Area of semicircle Area of right triangle ABC
Find the area of shaded region where a circle of radius 6cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm
Area of
Area of circle with centre
Area of sector
Area of shaded region
If radius is \(10\ cm \). Find the area of minor segment AQBP and area of major. Segment ALBQA (in \( cm^2\))
Area of minor segment
Area of major segment – area of minor segment
An elastic belt is placed around the rim of a pulley of radius 5cm. From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at p, 10cm from the point o Find the length of the belt that is still contact with the pulley.
Length of ADB
Find the area of the shaded region in figure, where APD, AQB, BRC and CSD are semicircles of diameter 14cm, 3.5cm, 7cm and 3.5cm respectively.
Area of shaded region = Area of semicircle APD + area of semicircle BRC2 ร area of semicircle AQB
All the vertices of a rhombus lie on a circle. Find the area of a rhombus, If the area of circle is 1256 cm
Diameter = Diagonal of the rhombus = 40 cm
The length of the minute hand of a clock is 14 cm. find the area swept by the minute hand in 10 minutes.
In hour the minute hand rotates . In minutes minute hand will rotate
Area of sector of angle
Four equal circles are described about the four corners of a square so that each touches two of the others. The shaded area enclosed between the circles being \(\dfrac{24}{7} \) sq cm. Find the radius of the circle.
Area of sector
Area enclosed by the circle = Area of square – (sum of the area of sector APS, BPQ, COQ, DRS)
But area enclosed
From (1) and (2)
The circumference of a circular park is 314 m. A 20 m wide concrete track runs round it. calculate the cost of laying turf in the park at 1.25 per sq m
Area of the plot
Area of a sector of a circle with radius \(14\ cm \) is \(154\ cm^2 \). Find the length of the corresponding arc of the sector.
If the difference between the circumference and the radius of the circle is 37 cm. Calculate the circumference
Circumference
If the perimeter of a circle is equal to that of a square, then the ratio of their areas
The area of the circle that can be inscribed in a square of side 6 cm is
Radius of circle
Area
The area of the square that can be inscribed in a circle of radius 8 cm is
Side of the square
Area