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Find the area of the shaded region, if PQ = 24, PR = 7 cm and O is the centre of the circle
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Radius
Area of semicircle
Area of
Area of shaded region
In the figure, ABCDEF is any regular hexagon. With different vertices A, B, C, D, E and F as the centres of circles with same radius r are drawn. Find area the of the shaded portion.
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Each interior angle
Area of 6 shaded region
In the figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm, to intersect the sides BC, CA and AB at their respective midpoints D, E and F. Find the area of the shaded region (Use \( \pi=3.14\))
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Area of sector
Area of shaded region
In the figure, sectors of two concentric circles of radii 7 cm and 3.5 cm are given. Find the area of shaded region. \(\left(use\ \pi=\dfrac{22}{7}\right) \)
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Area of outer sector
Area of inner sector
Difference
The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.
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+ length of arc
Area of sector
A horse is tied to a peg at one corner of a square shaped grass field of side 25 m by means of a 14 m long rope. Find the area of the part of the field in which the horse can graze \(\left[Take\ \pi=\dfrac{22}{7}\right] \)
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Area of the part of the field
Area of a sector of a circle of radius \(36\ cm \) is \(54\pi\ cm^2 \). Find the length of corresponding arc of sector.
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length of arc
The minute hand of a clock is \(\sqrt{21} \) cm long. Find the area swept by the minute hand on the face
of the clock from 7.00 am to 7.05 am.
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Area
The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at the speed of 66 km/hour ?
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Speed of the car km/hr
m/min
Speed of the car m/min
No. of revolutions
Find the area of the quadrant of that circle whose circumference is \(22\ cm\ \left(use\ \pi=\dfrac{22}{7}\right) \)
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Area
In the figure, the chord AB of a circle of radius 10 cm subtends an angle of 900 at the centre O. Find the area of the segment ACBA. (Take \(\pi=3.14 \))
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Area of sector
Area of
Area
A wheel has diameter 84 cm. Find how many complete revolutions must it make to cover 792 m.
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Circumference
Total no. of revolutions
How many times will the wheel of a car rotate in a journey of 2002 m, if the radius of the wheel is 49 cm?
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Circumference
Total rotation
A chord of a circle of radius 12 cm subtends an angle of 60° at the centre. Find the area of the corresponding segment of the circle. [use latex]\pi=3.14 [/latex] and \(\sqrt3=1.73 \) ]
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Area of segment – Area of
In the figure, a circle of radius 7 cm is inscribed in a square. Find the area of the shaded portion. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Area of circle
Area of square
Area of remaining potion
In the given figure, O is the centre of a circle. The area of sector OAPB is \(\dfrac{5}{18} \) of the area of the circle. Find x.
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Area of sector area of circle
Find the perimeter of the given figure, where AED is a semicircle and ABCD is a rectangle.
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Perimeter
A horse is placed for grazing inside a rectangular field 70 m by 52 m. It is tethered to one corner by a rope 21 m long. On how much area can it graze? How much area is left ungrazed?
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Area of grass grazed by hourse
The area of a circle inscribed in an equilateral triangle is \(154\ cm^2\). Find the perimeter of the triangle. [Take latex]\sqrt3=1.73 [/latex]]
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Peremeter
Four cows are tethered at the four corners of a square field of side 50 m such that each can graze the maximum unshaded area. What area will be left ungrazed? (Take \(\pi=3.14 \))
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Area of 4 quadrant
Area of square plot
Area of ungrazed land
In the figure, \(\triangle \)ABC is right angled at A, with AB = 6 cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Find the value of \(r_2 \) the radius of the inscribed circle.
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Area of Area of (OAC+OAB+BOC)
Find the area of the segment AYB in the figure, if the radius of the circle is 21 cm and \(\angle AOB=120^o \)
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Area of circle
Area of arc
Area of triangle
Area of segment
Three equal circles each of radius 6 cm touch one another as shown. Find the area enclosed between them.
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Area of equilateral
Area of the arc
Area of 3 sectors
Area of shaded portion
In an equilateral triangle of side 12 cm, a circle is inscribed touching its sides. Find the area of the portion of the triangle not included in the circle.
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Area of equilateral
In
Area of circle
Area of shaded region
Prove that the area of a circular path of uniform width k surrounding a circular region of radius r is \(\pi\ k(k+2r) \)
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Let radius of circular region
Radius of circular path of uniform with surrounding the circular region of radius,
Area of path
Find the area of the shaded region in the given figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid points P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. (Use \(\pi=3.14 \))
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Radius of circle
Area of shaded region
In the figure, OACBO represents a quadrant of a circle of radius 7 cm with centre at O. If OD = 5 cm, find the area of the shaded region.
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Area of quadrant
Area of
Area of shaded region
In the figure, diameter AB is 12 cm long. AB is trisected at points P and Q. Find the area of the shaded region.
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Area of shaded region
A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding minor segment of the circle. (Use \(\pi=3.14 \))
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In ,
Area of
Area of sector
Area of segment
In the figure, ABCD is a square of side 8 cm. CBED and ADFB are quadrants of circle. Find the area of the shaded region. (Use \(\pi=3.14 \))
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Area of quadrant
Area of
Shaded area
The length of a rope by which a cow is tethered is increased from 16 m to 23 m. How much additional area can the cow graze now? \(\left(use\ \pi=\dfrac{22}{7}\right) \)
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Additional area covered by
cow
The radii of two circles are 4 cm and 3 cm. Find the radius of the circle whose area is equal to the sum of the areas of the two circles. Also find the circumference of this circle.
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Area of new circle
Circumference
Find the area of the shaded region in the figure, if BC = BD = 8 cm, AC = AD = 15 cm and O is the centre of the circle. (Take \(\pi=3.14 \))
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area of circle
area of shaded portion
In a circle of radius 12 cm, an arc subtends an angle of 60° at the centre. Find
(i) Area of sector formed by the arc
(ii) Area of the segment formed by the corresponding chord.
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(i) Area of sector
(ii) Area of segment = Area of sector – area of OAB
In the figure, ABC is a triangle right angled at A. Find the area of the shaded region if AB = 6cm BC = 10 cm and I is the centre of incircle of \(\triangle \)ABC
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In
Area of
Area of
Area of circle
Area of shaded region
Find the area of the shaded region in the figure, where ABCD is a square of side 14 cm and four circles are each of same radius.
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Area of shaded portion
A square of side 4 cm is inscribed in a circle. Find the area enclosed between the circle and the square. \( \left[\pi=\dfrac{22}{7}\right]\)
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Area of shaded region