Question 1: Find the circumference and area of a circle of .
Answer:
Question 2: Find the circumference of a circle whose area is .
Answer:
Question 3: Find the area of a circle whose circumference is .
Answer:
Question 4: The circumference of a circle exceeds the diameter by . Find the circumference of the circle.
Answer:
Question 5: A horse is tied to a pole with long string. Find the area where the horse can graze.
Answer:
Question 6: A steel wire when bent in the form of a square encloses an . If the same wire is bent in the form of a circle, find the area of the circle.
Answer:
Let be the radius of the circle
Question 7: The diameters of the front and rear wheels of a tractor are and
respectively. Find the number of revolutions that rear wheel will make to cover the distance which the front wheel covers in
revolutions.
Answer:
Diameter of front wheel
Diameter of rear wheel
Distance covered by front wheel
Question 8: A copper wire when bent in the form of a square encloses an . lf the same wire is bent into the form of a circle, find the area of the circle.
Answer:
Let be the radius of the circle
Question 9: The circumference of two circles are in the ratio . Find the ratio of their areas.
Answer:
Let the radius of first circle
Let the radius of second circle
Question 10: The side of a square is . Find the area of circumscribed and inscribed circles.
Answer:
When a square is inscribed in the circle
Therefore diameter
Therefore radius of circle
Therefore are of circle
When the circle is inscribed in the square
Diameter
Question 11: The sum of the radii of two circles is and the difference of their circumferences is
. Find the diameters of the circles.
Answer:
Let the two radii be and
… … … … … i)
… … … … … ii)
From i) and ii)
Diameter of circles are and
Question 12: Find the area of the circle in which a square of is inscribed.
Take
Answer:
Side of square
Diameter of circle
Radius of the circle
Question 13: A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing would be at the rate of
per meter. Then, the field is to be thoroughly ploughed at the cost of
. What is the amount required to plough the field?
Take
Answer:
Cost of fencing
Circumference of the field
Area of the field
Therefore cost of ploughing
Question 14: If square is inscribed in a circle, find the ratio of the areas of the circle and the square.
Answer:
Hence the ratios of their area is
Question 15: A park is in the form of a rectangle . At the center of the park there is a circular lawn. The area of park excluding lawn is
. Find the radius of the circular lawn.
Take
Answer:
Let the radius of the circle
Area of the park
Are of circle
Question 16: The radii of two circles are and
respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.
Answer:
Let the radius of the circle
Question 17: The radii of two circles are and
respectively. Find the radius and area of the circle which has its circumference equal to the sum of the circumferences of the two circles.
Answer:
Let the radius of the circle
Question 18: A car travels 1-kilometer distance in which each wheel makes complete revolutions. Find the radius of its wheels.
Answer:
Let the radius of the wheel
Question 19: The area enclosed between the concentric circles is . If the radius of the outer circle is
, find the radius of the inner circle.
Answer:
Let the radius of the inner circle
Question 20: The wheel of a car is making revolutions per second. If the diameter of the wheel is
, find its speed in
. Give your answer, correct to nearest km.
Answer:
No. of revolutions per second
Radius of the wheel
Question 21: A sheet is long and
wide. Circular pieces of
in diameter are cut from it to prepare discs. Calculate the number of discs that can be prepared.
Answer:
Number of disks by length
No of disks by breadth
Therefore total number of disks that can be cut
Question 22: A copper wire when bent in the form of an equilateral triangle has . If the same wire is bent into the form of a circle, find the area enclosed.
Answer:
Let the side of the equilateral triangle
Let the radius of the circle
Question 23: A plot is in the form of a rectangle having semi-circle-on
as shown in the adjoining figure.
and
, find the area of the plot.
Answer:
Area of rectangle
Diameter of semi circle
Therefore Area of semi circle
Hence area of the park
Question 24: A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are and
, find, the area of the playground.
Take
Answer:
Area of rectangle
Question 25: The outer circumference of a circular race-track is . The track is everywhere
wide. Calculate the cost of leveling the track at the rate of
paise per square meter.
Take
Answer:
Let the outer
Therefore inner
Therefore area of track
Cost of leveling
Question 26: A rectangular piece is
long and
wide. From its four corners, quadrants of radii
have been cut. Find the area of the remaining part.
Answer:
Question 27: Four equal circles, each of , touch each other as shown in the adjoining figures. Find the area included between them.
Take
Answer:
Question 28: Four cows are tethered at four corners of a square plot of side , so that they just cannot reach one another. what area will be left ungrazed?
Answer:
Area of the square
Therefore Remaining
Question 29: A road which is wide surrounds a circular park whose circumference is
. Find the area of the road.
Answer:
Let the radius of the park
Circumference of park
Outer
Question 30: Four equal circles, each of radius a, touch each other. show that the area between the is .
Take
Answer:
Area of rectangle = (2a) \times (2a) = 4a^2
Question 31: Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions . Find the area of the remaining cardboard.
Take
Answer:
Area of board
Area of two cut outs
Remaining
Question 32: In the adjoining figure, a square is inscribed in a quadrant
of a circle. If
, find the area of the shaded region.
Answer:
,
is a square
Therefore shaded
Question 33: In the adjoining figure, is a right angled triangle in which
and
. Semi-circles are described on
and
as diameters. Find the area of the shaded region.
Answer:
Question 34: In the adjoining figure, and
is mid-point of
. Semi-circles are drawn on
and
as diameters. A circle with center
touches all the three circles. Find the area of the shaded region.
Answer:
Total area of large semi circle
Area of two smaller semi circles
Let the radius of the small circle
Therefore,
Therefore area of small circle
hence the shaded
Question 35: In the adjoining 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 and of the smallest is
, find i) the length of the boundary ii) the area of the shaded region.
Answer:
Question 36: In the adjoining figure, is the center of a circular arc and
is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place.
Take
Answer:
Question 37: In the adjoining figure, there are three semicircles, and
having diameter
each, and another semicircle
having a circle
with diameter
are shown. Calculate: (i) the area of the shaded region (ii) the cost of painting the shaded region at the rate of
, to the nearest rupee.
Answer:
i) Area of shaded area
ii) Therefore cost of painting shaded
Question 38: In the adjoining figure and
are two diameters of a circle perpendicular to each other and
is the diameter of the smaller circle. lf
, find the area of the shaded region.
Answer:
Area of larger circle
Area of smaller circle
Therefore shaded region
Question 39: In the adjoining figure, is a quadrant of a circle with center
and
. If
is
, find the area of the i) quadrant
an ii) shaded region.
Answer:
i) Area of quadrant
ii)
Question 40: For each of the two opposite corners of a square of side , a quadrant of a circle of
is cut. Another circle of
is also cut from the center as shown in the figure. Find the area of the remaining shaded portion of the square.
Take
Answer:
Question 41: Find the area of the shaded region in the adjoining figure, if , and
is center of the circle.
Take
Answer:
Therefore radius of the circle
Hence the shaded
Question 42: In the adjoining figure, is a square of side
. If
is a quadrant of a circle with center
, then find the area of the shaded region.
Take
Answer:
Question 43: In the adjoining figure,
is a rectangle, having
and
. Two sectors of
have been cut off. Calculate: i) the area of the shaded region ii) the length of the boundary of the shaded region.
Answer:
Question 44: A circle is inscribed in an equilateral triangle is side
, touching its Sides as shown in the adjoining figure. Find the radius of the inscribed circle and the area of the shaded part.
Answer:
Let the radius of the circle
Question 45: In the adjoining figure, shows the cross-section of railway tunnel. The of the circular part is
. If
, calculate: (i) the height of the tunnel (ii) the perimeter of the cross-section (iii) the area of the cross-section.
Answer:
i)
ii)
iii)