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Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is 8a cm? Give reasons for your answer.
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Radius,
Diameter,
Side of square
Perimeter
Is the following statement true? Give reasons for your answer. Area of a segment of a circle = area of the corresponding sector â€“ area of the corresponding triangle
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False
It is true only for a minor segment. In the case of a major segment area of the triangle will have to be added to the corresponding area of the sector.
Is the area of the circle inscribed in a square of side a \(cm,\ \pi a^2\ cm^2 \) ? Give reason for your answer
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False
Let a be the side of square
Diameter of circle = side of square = a
Radius of the circle
Area of the circle
Area of the circle is
In the figure, a circle is inscribed in a square of side 5 cm and another circle is circumscribing the square. Is it true to say that area of the outer circle is two times the area of the inner circle? Give reasons for your answer.
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True
Area of circle inner circle
area of outer circle
Ratio
In the figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.
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False
Diagonal of inner square = Diameter of circle = d
Let side of inner square be
But area of outer square
Is it true to say that area of a segment of a circle is less than the area of its corresponding sector ? Why ?
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False
It is true only in the case of mirror segment but in case of minor segment area is always greater than the area of sector.
In covering a distance s metres, circular wheel of radius r metres makes \(\dfrac{s}{2\pi r} \) revolutions. Is this statement true ? Why ?
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True
The distance covered in one revolution is
The numerical value of the area of a circle is greater than the numberical value of its circumference. Is this statement true ? Why ?
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If then numerical value of circumference is greater than numerical value of area of circle and if , area is greater than circumference.
If the length of an arc of a circle r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false ? Why ?
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False
Let two circles C and C’ of radius r and 2r with centres O and O’ respectively
â€¦(1)
…(2)
From eqn (1) and (2)
The areas of two sectors of two different circles with equals corresponding arc lengths are equal. Is this statement true ? Why ?
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False
It is true for arcs of the same circle. But in defferent circle it is not possible.
The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal ? Why ?
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False
It is true for arcs of the same circle. But in defferent circle it is not possible.
Is the area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) is \( \pi b^2\ cm^2\) ? Why ?
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The area of the largest circle than can be drawn inside a rectangle is where is the radius of the circle and it is possible when rectangle becomes a square.
Circumferences of two circles are equal. Is it necessary that their areas be equal ? Why ?
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True
If circumference of two circles are equal then their corresponding radii are equal so there areas will be equal.
Areas of two circles are equal. Is it necessary that their circumferences are equal ? Why ?
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True
If area of two circle are equal then their corresponding radii are equal so their circumference will be equal.
Is it true to say that area of a square inscribed in a circle of diameter \(p\ cm \) is \(p^2\ cm^2 \) ? Why ?
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False
When the square is inscribed in the circle, the diameter of a circle is equal to the diagonal of a square but not the side of the square.
A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/s. Calculate the number of complete revolutions the wheel makes in raising the bucket.
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Distance
circumference
No. of complete revolution
Diameters of three concentric circles are in the ratio 1 : 2 : 3. The sum of the circumferences of these circles is 264 cm. Find the area enclosed between second and third circles.
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Sum of circumference
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding (i) minor segment (ii) minor sector.
[Use latex]\pi =3.14 [/latex]]
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(i) Area of minor sector
(ii) Area of major sector
Find the area of both the segments of a circle of radius 15 cm, one of which makes an angle of 60Â° at the centre of the circle.
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Area of sector
Area of triangle
Minor segment = Area of sector – Area of triangle
Area of circle
Major segment (approx)
A chord 10 cm long is drawn in a circle whose radius is \(5\sqrt3\ cm \). Find the area of minor segment.
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Area of major segment = area of circle – area of minor segment
Area of minor segment
Area of major segment
A chord of a circle of radius 28 cm subtends an angle 45Â° at the centre of the circle. Find the area of the minor segment.
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Area
The perimeter of a sector of a circle with central angle 90Â° is 25 cm. Find the area of the minor segment of the circle.
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Area of minor segment
Find the area of the shaded portions of the following figure with given measurements :
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Area of sector
The diameter of a circular pond is 17.5 m. It is surrounded by a path of width 3.5 m. Find the area of the path.
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Radius
Radius of the park with path
Area of path
A sector is cut from a circle of radius 21 cm. The angle of the sector is 150Â°. Find the area of the sector.
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Length of the arc
Area
The diameter of the wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 km/hr ?
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Distance covered in 1 revolution
Speed
No. of revolutions
A playground is in the form of a rectangle having semicircles on the shorter sides. Find its area when the length of the rectangular portion is 80 m and the breadth is 42 m.
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Area = Area of rectangle + Area of semicircle
A bicycle wheel makes 500 revolutions in moving 22 km. Find the diameter of the wheel.
(take \(\pi=\dfrac{22}{7} \))
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Number of revolutions
Diameter
A plot is in the form of a rectangle ABCD having semicircle on BC as shown in the figure. The semicircle portion is grassy while the remaining plot is without grass. Find the area of the plot without grass where AB = 60 m and BC = 28 m.
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Area of plot = Area of rectangle + Area of semicircle
Find the area of a right angled triangle if the radius of its circumcircle is 2.5 cm and the long altitude drawn to the hypotenuse is 2 cm long.
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Hypotenuse
Altitude drawn to the hypotenuse
Area of right triangle
PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semicircles are drawn on PQ and QS as diameters. Find the perimeter of the shaded region.
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Perimeter of the shaded part
Area
OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. If the radius of the circle is 10 cm, find the area of the rhombus.
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Area
The difference between circumference and diameter of a circle is 135 cm. Find the radius of the circle. \( \left[Take\ \pi=\dfrac{22}{7}\right]\)
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The length of the minute hand of a clock is 7 cm. Find the area swept by the minute hand from 6.00 pm to 6.10 pm.
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Area
The sum of circumferences of two circles is 132 cm. If the radius of one circle is 14 cm, find the radius of the second circle.
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What will be the increase in area of a circle, if its radius is increased by 40%?
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New radius of
New area
increase
The radius of the wheels of a bus is 70 cm. How many revolutions per minute must a wheel make in order to move at a speed of 66 km/h?
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Circumference of the wheel
Speed of the wheel
Total resulution
resulution per minute
What will be the ratio of perimeters a square and a circle if their areas are equal?
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