CBSE Class 10 Maths 2024-25: Chapter 11 Areas Related to Circle Competency-Based Questions with Answers; Download Free PDF

As the CBSE Class 10 board exams get closer, students need to understand the new exam pattern. Starting in the 2024-25 school year, CBSE will include 50% more competency-based questions. These questions will be both multiple choice and written, focusing on how to use what students have learned in real-life situations.

This article explores Chapter 11 Areas Related to Circle. It highlights key competency-based questions and provides answers to help students succeed.

Understanding Competency-Based Questions in Chapter 11 Areas Related to Circle

Competency-based questions are designed to see how well students can apply their knowledge in everyday life. They can come in different forms, such as case studies, true-false questions, gap-filling tasks, and long or short answer questions.

Competency-based questions in Chapter 11: Areas Related to Circle  go beyond memorization, encouraging critical thinking and problem-solving. These questions help students grasp concepts deeply by applying them to real-world scenarios.

CBSE Class 10 Maths Chapter 11: Areas Related to Circle Important Competency-Based Questions

Multiple Choice Questions

Q.1 Shown below is a circle with centre O. The area of the minor sector SOT is 7 cm² .

Answer. (3)

Q.2 In the figure given below, O is the centre of the circle. XYZ is an arc on the circle subtending an angle of 45° at the centre.

Answer. (2)

Q.3 In the figure shown below, C is the centre of the circle. The area of the shaded sector

What is the measure of angle z ?

1. 135°
2. 200°
3. 225°
4. (cannot be determined as the radius of circle is not given)

Answer. (3)

Q.4 Shown belowisacircle with centre O and radius28cm. Chord RSsubtends anangle of 90° at O.

1. 224 cm²
2. 616 cm²
3. 1848 cm²
4. 2240 cm²

Answer. (4)

Q.5 In the circle shown below, O is the centre. MN is a chord which subtends an angle of 90° at the centre. The area of the shaded region is 72 cm² .

1. 6√7 cm
2. 6√28 cm
3. 84 cm
4. 252 cm

Answer. (1)

Q.6 A circular pond needs to be fenced along its circumference. One-fourth of the fencing is already done, which cost Rs 750 at the rate of Rs 50 per metre. How many metres of the pond still need to be fenced?

1. 15
2. 20
3. 45
4. 60

Answer. (3)

Q.7 Which of the following information is NOT sufficient to differentiate between minor and major sector of a circle?

1. the angle subtended at the centre
2. the radius of the circle
3. the area of the sector
4. the length of the arc

Answer. (2)

Free Response Questions

Q.8 In a circular agricultural field, a sector subtending an angle of 120° at the centre is dedicated to growing sugarcane.

If the radius of the circular field is 30 meters, what is the area of the land used for growing sugarcane? Show your work.

(Note: Take π as 3.14.)

Answer. Finds the area of the sector used for growing sugarcane as:

Q.9 Anjali got the following question in her class test.

"A 13 cm chord of a circle subtends an angle of 60° at the centre. Find the area of the minor segment."

After the test, she went to the teacher and said, "The question cannot be answered as it doesn't mention the radius of the circle".

Is Anjali right or wrong? Give a valid reason for your answer.

Answer. Writes that Anjali is wrong and gives a reason. For example, since the chord extends an angle of 60° at the centre, it forms an equilateral triangle with the radii and hence, the radius is 13 cm.

Q10 Shown below is a circle with centre O. The area of the shaded region is 294π cm² .

Answer. 

area of the circle as:

294π × 6 = 1764π cm²

(Award full marks if radius is calculated first and then the area of the circle.)

Q.11 Find the length of an arc which subtends an angle of 80° at the centre of a circle with radius 63 cm. Show your work.

Answer. 

Q.12 The length of an arc of a circle is 22 cm and its radius is 21 cm.

What is the area of the sector formed by the arc? Show your work.

Answer. Assumes the angle of the sector as θ and writes the equation as:

Case Study

Answer the questions based on the given information. An archery target board consists of three concentric circles with centre O as shown below. The innermost circle has a radius of 7 cm, the middle circle has a radius of 14 cm, and the outer circle has a radius of 28 cm. The target board is divided into four equal parts by AC and BD, which are the diameters of the outermost circles. The scoring system for the game is as follows:
Area LIO: 10 points
Area KJIEFG: 7
points Area ABEH: 4 points

Q.13 Find the area of the sector in which 10 points can be scored. Show your work.

Answer. Uses the expression for the area of a sector to find the area of the part LIO as:

Q.14 If the target lands on the boundary of the 4 points scoring area, a deduction of 1 point occurs, resulting in a score of 3 points. Find the length of the boundary in which 3 points can be scored. Show your work.

Answer. Finds the length of arc of middle circle as:

Finds the length of arc of outer circle as:

Finds the length of boundary in which 3 points can be scored as:
44 + 22 + 2(28 - 14) = 94 cm

Q.15 Find the area KJIEFG. Show your work.

Answer. Finds the area of the semicircle in the middle region as:

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