Note: Take until and unless stated otherwise.
Question 1: Find the circumference and area of a circle whose radius is: (i) (ii)
(iii)
Answer:
(i)
(ii)
(iii)
Question 2: Find the circumference and area of a circle whose diameter is: (i) (ii)
Answer:
(i)
(ii)
Question 3: Taking , find the circumference and area of a circle whose radius is: (i)
(ii)
(iii)
Answer:
(i)
(ii)
(iii)
Question 4: Find the area of a circle whose circumference is: (i) (ii)
Answer:
(i)
(ii)
Question 5: Find the radius and circumference of a circle whose area is: (i) (ii)
Answer:
(i)
(ii)
Question 6: Taking , find the radius and circumference of a circle whose area is: (i)
(ii)
(iii)
Answer:
(i)
(ii)
(iii)
Question 7: A rectangular sheet of acrylic is by
. From it,
circular buttons, each of diameter
have been cut out. Find the area of the remaining sheet.
Answer:
Area of rectangular sheet of acrylic
Area of 56 buttons
Area of remaining sheet
Question 8: A rectangular ground is
long and
broad. In the middle of the ground, there is a circular tank of
. Find the cost of turfing the remaining portion at the rate of
sq. meter.
Answer:
Area of rectangular ground
Area of circular tank
Area of remaining sheet
Cost of turfing
Question 9: Find the area of a circle inscribed in a square of side
.
Answer:
The diameter of the circle = Side of the square
Question 10: A wire is in the form of a circle of . It is straightened and bent into the form of a square. What is the length of the side of the square?
Answer:
Question 11: A wire is in the form of a square of side . It is straightened and bent into a circle. What is the radius of the circle so formed?
Answer:
Question 12: A wire when bent in the form of a square, encloses an area of . If the same wire is bent to form a circle, what will be the radius of the circle so formed?
Answer:
Radius of the circle
Question 13: The radius of a wheel is . Find the distance travelled by it m: (i) one revolution (ii)
revolutions
Answer:
(i) Distance traveled in one revolution
(ii) Distance traveled in revolution
Question 14: How many revolutions would a cycle wheel of diameter make to cover a distance of
?
Answer:
Circumference of the wheel
Number of revolution
Question 15: The wheel of motor-cycle, in diameter. is making
revolutions in every
seconds. Find the speed of the motor-cycle in km per hour.
Answer:
Distance covered by the motor cycle in 1 sec
Speed of motor cycle
Question 16: The wheel of a car rotates times in travelling a distance of
. Find the diameter of the wheel.
Answer:
Circumference of the wheel
Diameter of the wheel
Question 17: The shape of a park is a rectangle bounded by semi-circles at the ends, each of
, as shown in the adjoining figure. Find the area and the perimeter of the park.
Answer:
Area
Perimeter
Question 18: Find the area of the space enclosed by two concentric circles of radii and
.
Answer:
Enclosed space
Question 19: The diameter of a circular park is . On its outside, there is a path
wide, running around it. Find the cost of turfing the path at
per square meter.
Answer:
Enclosed space
Cost of turfing
Question 20: A circular field of has a circular path of uniform width of
along and inside its boundary. Find the cost of paving the path at
per sq. meter.
Answer:
Enclosed space
Cost of turfing
Question 21: The area of a circular pond is . A path of width
runs all around it, on the outside. Calculate the area of the path.
Answer:
Area of the path
Question 22: The area of a circular grass lawn is . A path of uniform width was laid all around it, on the outside. The area of the path is
. Find (i) the radius of the grass lawn; (ii) the width of the path.
Answer:
Radius of circular grass lawn
Therefore
Area including the path
Radius of circular grass lawn + Path
Therefore the width of the path
Question 23: The outer edge of a circular running track is long. It is widened by
all around on the outside. Find the area of the widened part.
Answer:
Radius of circular running track
Area of the path
Question 24: The area of a ring is and the radius of the outer circle is
. Find: (i) the area of the smaller circle (ii) the width of the ring (Take
).
Answer:
Given:
Area of smaller circle
Width of the path
Question 25: Find the area of the shaded region in the adjoining figure, the radii of bigger and smaller quadrants being
and
respectively.
Answer:
Area of the shaded region
Question 26: The perimeter and the area of the shaded region in the adjoining figure, it being given that OAB is an equilateral triangle of side
and one end is a semi-circle on AB as diameter.
Answer:
Perimeter of the figure
Area of the shaded region
Note: The height of the triangle
Question 27: Find the perimeter and the area of the adjoining figure, it being given that
and one end of the figure is a semi-circle with
as diameter (Take
).
Answer:
Area of the figure
Perimeter
Question 28: Find the area of the shaded region in each of the following figures:
Answer:
(i) Area of the shaded region
(ii) Area of the shaded region
(iii) Area of the shaded region
Question 29: Find the area of the shaded region in each of the following figures:
Answer:
(i) Area of the shaded region
(ii) Area of the shaded region
(iii) Area of the shaded region
(iv) Area of the shaded region
Question 30: Find the area of the shaded region in each of the following figures:
Answer:
(i)
Area of the shaded region
(ii) Area of the shaded region