CBSE Class 10 Maths Chapter 12 Important Questions with Answers: Areas Related to Circles

CBSE Class 10 Maths Chapter 12 Important Questions with Answers: Areas Related to Circles is a part of the Sixth unit Mensuration. In this article, get the important questions from the chapter with the answers in the pdf.

CBSE Class 10 Maths Chapter 12 Important Questions with Answers: This article enlists the important questions from Chapter 12 of CBSE Class 10 i.e Areas Related to Circles. For the candidates preparing to attempt CBSE Class 10 Mathematics board examinations, these important questions will ensure that all varieties of questions from different concepts are well-covered. In other words, these important questions will act like a checklist with a variety of questions with varying difficulty from the chapter.

Chapter 12th is a part of the unit Mensuration which has a total weightage of 10 marks.

The prescribed topics to be covered under CBSE Class 10 Maths Chapter 12 Areas related to Circles are as follows: Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only.)

The other chapter in Unit VI Mensuration is Surface Areas & Volumes.

Students can view the detailed CBSE Class 10 Maths Syllabus 2022-2023 by clicking on the link below:

CBSE Class 10 Maths Syllabus 2022-2023

CBSE Class 10 Maths Chapter 12 Important Questions

MULTIPLE CHOICE QUESTIONS

Q1. A display board is in the shape of a circle. While designing the board, if diameter of the board is increased by 40% from the previous design, then the area will be increased by

(a.) 40%

(b.) 80%

(c.) 96%

(d.) 45%

Q2. If θ is the angle in degrees of a sector of a circle of radius r units, then the area of the sector is

Q3. Area of a square is the same as the area of a circle. What will be the ratio of their perimeters?

(a.) 1 : 1

(b.) π : √2

(c.) 2 : √π

(d.) None of these

Q4. Area of the largest triangle inscribed in a semi-circle of radius r units is

Q5. Which ratio is denoted by a constant known as π

(a.) Diameter/Circumference

(b.) Area/Circumference

(c.) Circumference/Diameter

(d.) Area/Diameter

Q6. If the circumference of a circle and the perimeter of a square are equal, then the

(a.) Area of the circle = Area of the square

(b.) Area of the circle > Area of the square

(c.) Area of the circle < Area of the square

(d.) We cannot definitely say about the relation between area of the circle and the square

Q7. The ratio of areas of two circles whose ratio of circumferences is in the ratio of 3 : 1 will be

(a.) 3 : 1

(b.) 1 : 3

(c.) 1 : 9

(d.) 9 : 1

Q8. The minute hand of a clock is 14 cm long . The area described by it on the face of the clock in 5 minutes is

(a.) 51.33 cm²

(b.) 15.33 cm²

(c.) 21.15 cm²

(d.) 12.35 cm²

Q9. Radii of two circles are 4 cm and 3 cm respectively. There is another circle, which is having area equal to the sum of the areas of two circles whose radii are known. Find the diameter (in cm) of the third circle.

(a.) 5

(b.) 7

(c.) 0

(d.) 14

Q10. Find the area of the largest circle that can be drawn inside a rectangle with length a cm and breadth b cm. (a > b).

VERY SHORT ANSWER QUESTIONS

Q1. Say the following statement is “True” or “False”. Write the reason for your answer.

“Area of a segment of a circle is less than the area of its corresponding sector.”

Q2. Find the circumference of a circle whose area is 314 cm². (Given π = 3.14)

Q3. Find the area of a sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Q4. State the following statement is “True” or “False”. “If the perimeter and area of a circle are numerically equal, then the radius of the circle is 2 units”.

Q5. Area of a sector is one- twelfth that of the complete circle. Find the angle of the sector.

Q6. Find the area of a sector of a circle of radius 28 cm and central angle 45 ̊. (Take π = 22/7)

Q7. Rear wheel of a motor cycle is of radius 35 cm. It is assumed that the speed of the motor cycle is fully depend on the rpm of the rear wheel and no loss of energy. How many revolutions per minute (rpm) must the wheel make so as to keep a constant speed of 66 km/hr. (Take π = 22/7)

Q8. An arc of a circle of length 5π cm bounds a sector whose area is 20π cm². Find the radius of the circle.

Q9. If the perimeter of a semi-circular protractor is 66 cm, find the length of the straight-line part of the protractor. (Take π = 22/7)

Q10. A chord of a circle of radius 10 cm subtends right angle at the centre of the circle. What will be the area of the corresponding major sector? (Given π = 3.14)

SHORT ANSWER QUESTIONS (2 MARKS)

Q1. The circumference of a circle exceeds the diameter by 16.8 cm. Find the radius of the circle.

Q2. A race track is in the form of a ring whose inner circumference is 352m and the outer

circumference is 396m.Find the width of the track.

Q3. A wheel has diameter 84cm.Find how many complete revolutions it must take to cover 792m.

Q4. A car travels 1 km distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.

Q5. A bicycle wheel makes 5000 revolutions in moving 11km.Find the diameter of the wheel.

Q6. Find the diameter of the circle whose area is equal to the sum of the areas of two circles of diameters 20cm and 48cm

SHORT ANSWER QUESTIONS (3 MARKS)

Q1. If the difference between the circumference and area of a circle is37 cm, find its area.

Q2. Calculate the perimeter of an equilateral triangle, if it is inscribed in a circle with area 154 Cm²

Q3. A chord AB of a circle of radius 10 cm makes a right angle at the centre of the circle. Find the area of the minor and major segments.

Q4. Four poles are erected at four corners of a rectangular field of dimensions 80 m by 50 m. Vasanthi tethered a cow at one corner of the field with a rope. After tying the length of rope from pole to cow is 7 m and Rajan tethered a buffalo at another pole of the same field and the length of rope from pole to animal is 6.3 m.

Answer the following questions.

1. How much area of the rectangular field did the cow graze?
2. Find the ratio of grazing areas of the field by the cow and buffalo.

Q5. A square is inscribed in a circle. Calculate the ratio of area of circle to that of square.

LONG ANSWER QUESTIONS

Q1. A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.

Q2. The inner circumference of a circular track is 220m. The track is 7m wide everywhere. Calculate the cost of putting up a fence along the outer circle at the rate of Rs.2 per metre.

Q3. Find the area of the minor segment of a circle of radius 42 cm, if length of the corresponding arc is 44 cm.

DOWNLOAD Answers to CBSE Class 10 Maths Chapter 12 Important Questions

There are fifteen chapters in CBSE Class 10 Mathematics syllabus for 2022-23. These chapters are  divided under seven different units.

To check how well your preparation is in sync with the board’s evaluation schemes, check:

CBSE Class 10 Mathematics (Standard) Sample Paper 2023

CBSE Class 10 Mathematics (Basic) Sample Paper 2023

All the best!