*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