Enhanced Curriculum Support

SecA

1. Find the circumference of a circle with a radius of 7 cm.

2. What is the area of a circle with a diameter of 14 cm?

3. If the radius of a circle is doubled, by what factor does the area increase?

4. The circumference of a circle is 44 cm. Find its radius.

5. What is the area of a sector with a central angle of 90° and a radius of 14 cm?

6. A square OABC is inscribed in a quadrant OABQ of a circle as shown in the figure. If OA = 14 cm, find the area of the shaded region.

SecB

1. The radius of a circular garden is 10.5 m. Calculate the cost of fencing it at ₹20 per meter.

2. Find the area of a sector of a circle with a central angle of 60° and a radius of 7 cm.

3. A chord of a circle subtends an angle of 90° at the center. If the radius of the circle is 14 cm, find the length of the chord.

4. The area of a circular park is 314 m². Find its circumference.

5. If the radius of a circle is 21 cm, what is the area of the minor segment formed by a chord of length 21 cm?

6. The area of a n equilateral triangle is 49 cm2. Taking each angular point as centre, circles are drawn with radius equal to half length of the side of the triangle. Find the area of triangle not included in the circles.

SecC

1. Find the area of a ring (annular region) formed between two concentric circles of radii 14 cm and 21 cm.

2. A sector of a circle with a radius of 28 cm has a central angle of 120°. Find the area of the sector and the length of the arc.

3. The circumference of a circle is 132 cm. Find the area of the circle.

4. A circular park has a diameter of 42 m. A path 3.5 m wide is constructed around the park. Find the cost of paving the path at ₹100 per square meter.

5. The area of a circular field is 1386 m². A path of width 7 m is constructed around the field. Find the area of the path.

6. A bicycle wheel makes revolutions per minute to maintain a speed of 8.91 km per hour. Find the diameter of the wheel.

7. Four equal circle are described about the four corners of a square so that each touches two of the others, as shown in teh figure. Find the area of the shaded region, each side of the square measuring 14 cm.

SecD

1. A circular pond has a radius of 35 m. A path of width 7 m is constructed around the pond. Find the area of the path and the cost of paving it at ₹60 per square meter.

2. A chord of a circle of radius 20 cm subtends an angle of 120° at the center. Find the area of the corresponding major and minor segments. (Use π = 3.14)

3. The area of a sector of a circle of radius 7 cm is 77 cm². Find the length of the corresponding arc and the angle of the sector.

4. In a circular park of radius 21 m, two perpendicular pathways are constructed such that they divide the park into four equal parts. Find the area of the pathways if the width of each pathway is 3.5 m.

5. A circular park has a radius of 35 m. A path of width 7 m is constructed outside the park. Find the area of the park, the path, and the total cost of fencing the outer edge of the path at ₹50 per meter.

6. A play ground is in the form of a rectangle havign semi-circles on the shorter sides as shown in the figure. Find its area when the length of the rectangular portion is 38 m and the breadth is 10 m. [use π = 3.14]

Problem1

Situation: A farmer has a circular field, and he needs to install a fence around it. The radius of the field is 21 meters. He also wants to plant grass in the entire field.

1. The farmer wishes to buy fencing material at ₹150 per meter and plant grass at the rate of ₹10 per square meter. Calculate the total cost of fencing the field and planting grass.

Problem2

Situation: In a school playground, a circular track with a radius of 35 meters is being designed for running events. The track is to be laid out around a central circular lawn.

1. If the width of the track is 5 meters, find the area of the track. The school wants to cover the track with rubber flooring, which costs ₹200 per square meter. Calculate the total cost for covering the track.

Problem3

Situation: A garden has a circular pond with a radius of 7 meters. Surrounding the pond is a circular walking path of uniform width. The total radius (pond + path) is 10 meters.

1. Calculate the area of the walking path. If the walking path needs to be paved at ₹50 per square meter, what will be the total cost for paving the path?

Problem4

Situation: A circular logo with a radius of 6 cm is to be designed for a company. The design requires the use of gold plating along the circular boundary of the logo.

1. Find the length of the boundary of the logo. If the cost of gold plating is ₹25 per centimeter, calculate the total cost of gold plating the boundary.

Problem5

Situation: A circular park has a diameter of 84 meters. The park committee plans to build a circular fountain at the center, with a radius of 14 meters.

1. Find the area of the park excluding the area of the fountain. If the remaining area is to be covered with grass at ₹12 per square meter, calculate the total cost of covering the area with grass.

Q1

1. A wire is bent in the form of a square of area 484 cm². If the same wire is bent to form a circle, find the area of the circle. Also, find the difference in areas between the square and the circle.

2. Two sectors of a circle have equal areas but different central angles. If the radius of one sector is 21 cm and the radius of the other is 28 cm, find the ratio of their central angles.

3. A circle of radius 7 cm is inscribed in a square. Find the area of the square that lies outside the circle.

4. A wire is bent in the form of a square of area 484 cm². If the same wire is bent to form a circle, find the area of the circle. Also, find the difference in areas between the square and the circle.

Q2

1. Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.

2. A circle is inscribed in an equilateral triangle of side 24 cm. Find the area of the triangle that is not covered by the circle.

3. A chord of a circle with a radius of 21 cm subtends an angle of 120° at the center. Find the area of the shaded region between the chord and the arc if the area of the major sector is twice the area of the minor sector.

4. A circle is inscribed in an equilateral triangle of side 24 cm. Find the area of the triangle that is not covered by the circle. (Use π = 3.14 and √3 = 1.732)

Q3

1. On a square cardboard sheet of area 784 cm2, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.

2. Floor of a room is of dimensions 5m x 4m and it is covered with circular tiles of diameters 50 cm each as shown infigure. Find area of floor that remains uncovered with tiles, (use π = 3.14)

3. An archery target has three regions formed by three concentric circles as shown in figure. If the diameters of the concentric circles are in the ratio 13, then find the ratio of the areas of three regions.

4. Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of 176 m.

5. The area of a circular garden is equal to the area of a square field. If the radius of the circular garden is 14 m, find the side length of the square field. Which field has a greater perimeter?

Q4

1. All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 cm2, (use π = 3.14)

2. The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6 : 05 am and 6 : 40 am

3. Area of a sector of central angle 200° of a circle is 770 cm2. Find the length of the corresponding arc of this sector.

4. A circular park is surrounded by two concentric circular paths, where the inner path has a radius of 35 m and the outer path has a radius of 42 m. If the cost of paving the inner path is ₹40 per square meter and the cost of paving the outer path is ₹50 per square meter, find the total cost of paving both paths.

Q5

1. The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?

2. Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of 90° at the centre.

3. Four circular cardboard pieces of radii 7 cm are placed on a paperin such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces

4. A rectangular field is 44 m long and 33 m wide. Two semi-circular tracks are constructed on the shorter sides of the rectangle, touching its width. Find the area of the total track and the difference between the perimeter of the rectangle and the perimeter of the semi-circular tracks.

Questions

1. If the length of an arc of a circle of radius 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?

2. Find the radius of a circle whose circumference is equal to the sum of the circumference of two circles of radii 15 cm and 18 cm.

3. Find the area of a sector of a circle of radius 28 cm and central angle 45°.

4. The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make, so as to keep a speed of 66 km/h?

5. A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m x 16 m. Find the area of the field in which the cow can graze.

6. Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°.

7. A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then find the area of the road

8. A piece of wire 20 cm long is bent into the from of an arc of a circle, subtending an angle of 60° at its centre. Find the radius of the circle.

9. The area of a circular playground is 22176 m2.Find the cost of fencing this ground at the rate of ₹ 50 per m.

10. The diameters of front and rear wheels of a tractor are 80 cm and 2m, respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.

11. Sides of a triangular field are 15 m, 16m and 17m. with the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.

12. Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a centrel angle of 60°. (use π = 3.14)

13. A circular pond is 17.5 m is of diameter. It is surrounded by a 2m wide path. Find the cost of constructing the path at the rate of ₹ 25 Per m2?

14. Three circles each of radius 3.5 cm are drawm in such a way that each of them touches the other two. Find the area enclosed between these circles.

15. Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Question 1

The Ashoka chakra is a depiction of Dharma chakra, a wheel represented with 24 spokes. It is so called because it appears on a number of edicts of Ashoka. Most prominent among which is the lion capital of Ashoka. It is most visible in the middle of the flag of India. This is also India’s highest peace time military decoration awarded for valour, courageous action or self -sacrifice.

On the occasion of Independence Day, the students of our school made a huge flag with Ashoka chakra in the middle on the ground using flowers, colours and ribbons. The spokes and outer edge of the chakra was made by ribbon. The length of the ribbon used in the outer edge (circumference) was 440 cm.

Based on your understanding of the above case study, answer all the five questions below

1. What is the radius of each spoke?

2. What is the angle between two consecutive spokes?

3. What is the total length of the ribbon used here for spokes and circumference?

4. The area on the ground between two consecutive spokes is approximately?

5. What will be the cost of flowering the total area inside the chakra at the rate of rupees 200 per m2?

Question 2

During summer vacation Mohini had gone to sea beach with her parents. There she noticed a tall tower. She asked her father about the tower. Her father told that it is a Light House. She wanted to know about its function. Her father told that it is a tower with a bright light at the top located at an important or dangerous place regarding navigation. The two main purposes of light house are to serve as a navigational aid and to warn boats of dangerous areas. It is like traffic signal.

To test her knowledge, her father asked the following questions. If the focus of light emitted by it can travel up to 70 km and the angle between two rays at the extreme ends is one sixth of a complete angle, then

Based on your understanding of the above case study, answer all the five questions below:

1. Find the angle between two rays OA and OB as shown in the figure

2. Find the total area that it will cover on the surface of

3. If OBXD is a sector of radius 1km, then what is the length of chord BD

4. If OM is perpendicular to BD, then what is its length?

5. What is the area of segment BXD?