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AREAS RELATED TO CIRCLES - MCQs

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Maths — AREAS RELATED TO CIRCLES

50 Questions Class 10 MCQs

The formula for the area of a circle of radius \(r\) is

a a. \(2\pi r\) b b. \(\pi r^2\) c c. \(\pi d\) d d. \(\frac{1}{2}\pi r^2\)

If the radius of a circle is doubled, its area becomes

a a. double b b. triple c c. four times d d. eight times

The value of \(\pi\) generally used in NCERT problems is

a a. 3 b b. \(\frac{21}{7}\) c c. \(\frac{22}{7}\) d d. 3.5

A sector of a circle is bounded by

a a. two chords b b. two tangents c c. two radii and an arc d d. a chord and an arc

The total angle at the centre of a circle is

a a. \(90^\circ\) b b. \(180^\circ\) c c. \(270^\circ\) d d. \(360^\circ\)

The area of a sector of angle \(\theta^\circ\) and radius \(r\) is

a a. \(\theta \pi r^2\) b b. \(\frac{360}{\theta}\pi r^2\) c c. \(\frac{\theta}{360}\pi r^2\) d d. \(\frac{\theta}{180}\pi r^2\)

A sector whose angle is less than \(180^\circ\) is called

a a. major sector b b. minor sector c c. segment d d. arc

A sector whose angle is more than \(180^\circ\) is called

a a. minor sector b b. semicircle c c. major sector d d. segment

A segment of a circle is bounded by

a a. two radii b b. a radius and an arc c c. a chord and an arc d d. two chords

The smaller region formed by a chord and an arc is called

a a. major segment b b. minor segment c c. sector d d. semicircle

The area of a minor segment is found by

a a. adding triangle area to sector area b b. subtracting triangle area from sector area c c. subtracting sector area from circle area d d. adding sector area to circle area

The area of a major segment is

a a. area of circle - area of major sector b b. area of sector - area of triangle c c. area of circle - area of minor segment d d. area of triangle - area of sector

Which of the following is a chord of a circle?

a a. Diameter b b. Radius c c. Tangent d d. Arc

The longest chord of a circle is

a a. radius b b. tangent c c. diameter d d. arc

If the diameter of a circle is \(14\) cm, its radius is

a a. 14 cm b b. 28 cm c c. 7 cm d d. 21 cm

The area of a semicircle of radius \(r\) is

a a. \(\pi r^2\) b b. \(\frac{1}{2}\pi r^2\) c c. \(2\pi r^2\) d d. \(\pi r\)

The unit of area related to circles is

a a. cm b b. cm\(^3\) c c. cm\(^2\) d d. m

If the radius of a circle is zero, its area is

a a. \(\pi\) b b. 1 c c. 0 d d. undefined

A quadrant of a circle subtends an angle of

a a. \(45^\circ\) b b. \(60^\circ\) c c. \(90^\circ\) d d. \(180^\circ\)

The area of a quadrant of radius \(r\) is

a a. \(\pi r^2\) b b. \(\frac{1}{2}\pi r^2\) c c. \(\frac{1}{4}\pi r^2\) d d. \(2\pi r^2\)

Which concept is most useful in finding shaded regions?

a a. Volume b b. Area subtraction c c. Linear equations d d. Probability

The boundary length of a circle is called

a a. area b b. diameter c c. circumference d d. radius

The formula for circumference of a circle is

a a. \(\pi r^2\) b b. \(2\pi r\) c c. \(\pi d^2\) d d. \(\frac{1}{2}\pi r\)

The area of a sector is directly proportional to

a a. radius b b. diameter c c. central angle d d. circumference

A circle is divided into equal sectors. The areas of the sectors are

a a. unequal b b. proportional to radius c c. equal d d. zero

The region enclosed between two concentric circles is called

a a. sector b b. segment c c. ring d d. arc

The area of a ring depends on

a a. inner radius only b b. outer radius only c c. difference of radii d d. difference of squares of radii

In exams, shaded region problems mostly involve

a a. only triangles b b. only rectangles c c. only circles d d. combination of figures

Which value of \(\pi\) is used when radius is a multiple of 7?

a a. 3 b b. \(\frac{22}{7}\) c c. 3.14 d d. 2.17

The area of a sector with angle \(180^\circ\) is

a a. full circle b b. half circle c c. one-third circle d d. quadrant

Which figure is formed by a diameter and an arc?

a a. sector b b. semicircle c c. segment d d. quadrant

The area of a minor segment is always

a a. greater than half the circle b b. equal to half the circle c c. less than half the circle d d. equal to the triangle area

To find the area of a major sector, we usually

a a. add triangle area b b. subtract minor sector from circle c c. subtract triangle from sector d d. add all parts

Which mathematical idea links angles and areas in circles?

a a. Linear equations b b. Proportionality c c. Probability d d. Statistics

A wheel of radius \(r\) completes one full rotation. The area covered relates to

a a. circumference b b. diameter c c. area of circle d d. area of square

The region enclosed by a chord and the major arc is

a a. minor segment b b. major segment c c. sector d d. semicircle

Which topic is essential before studying this chapter?

a a. Trigonometry b b. Circles basics c c. Probability d d. Statistics

Area related to circles belongs to which branch of mathematics?

a a. Algebra b b. Geometry c c. Arithmetic d d. Calculus

If the radius is given in metres, the area will be in

a a. m b b. m\(^2\) c c. cm\(^2\) d d. km

Which of the following is NOT a part of this chapter?

a a. Area of sector b b. Area of segment c c. Surface area of sphere d d. Area of circle

The area of a circle increases when

a a. radius decreases b b. radius increases c c. diameter is zero d d. centre changes

A semicircle subtends an angle of

a a. \(90^\circ\) b b. \(120^\circ\) c c. \(180^\circ\) d d. \(360^\circ\)

The formula \(\frac{\theta}{360}\times \pi r^2\) is based on

a a. addition b b. subtraction c c. ratio d d. multiplication only

In shaded region problems, the first step should be

a a. substitute values b b. write the answer c c. identify required region d d. choose value of \(\pi\)

Which shape helps in finding segment area?

a a. rectangle b b. square c c. triangle d d. trapezium

The area of a circle is zero when

a a. diameter is maximum b b. radius is negative c c. radius is zero d d. \(\pi=0\)

Which figure gives maximum area for a fixed perimeter?

a a. square b b. rectangle c c. circle d d. triangle

The formula for area of a ring is

a a. \(\pi(R+r)^2\) b b. \(\pi(R^2-r^2)\) c c. \(2\pi(R-r)\) d d. \(\pi(R-r)^2\)

Which problems are most common in board exams from this chapter?

a a. Proofs only b b. Constructions only c c. Numerical problems d d. Graphs only

This chapter mainly strengthens which skill?

a a. Memorisation b b. Drawing c c. Logical application of formulas d d. Speed writing

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Frequently Asked Questions

A circle is the locus of all points in a plane that are at a fixed distance, called the radius, from a fixed point known as the centre.

The area of a circle is the region enclosed by its circumference and is calculated using the formula \(A = \pi r^2\).

\(\pi\) is a constant representing the ratio of the circumference of a circle to its diameter, commonly taken as \(\frac{22}{7}\) or 3.14.

A sector is the region bounded by two radii and the arc between them.

A minor sector is the smaller sector formed when the central angle is less than \(180^\circ\).

A major sector is the larger sector formed when the central angle is greater than \(180^\circ\).

The area of a sector is \(\frac{\theta}{360^\circ} \times \pi r^2\), where \(\theta\) is the central angle.

The angle at the centre determines what fraction of the circle the sector occupies, directly affecting its area.

A segment is the region bounded by a chord of a circle and the corresponding arc.

A minor segment is the smaller region formed between a chord and the corresponding minor arc.

A major segment is the larger region formed between a chord and the corresponding major arc.

Area of minor segment = Area of corresponding sector - Area of the triangle formed by the radii and chord.

Area of major segment = Area of the circle - Area of the minor segment.

A triangle helps remove the straight-line portion inside the sector, leaving only the curved region of the segment.

A chord is a line segment joining any two points on the circumference of a circle.

AREAS RELATED TO CIRCLES - MCQs

Maths — AREAS RELATED TO CIRCLES

Frequently Asked Questions

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AREAS RELATED TO CIRCLES – Learning Resources

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AREAS RELATED TO CIRCLES - MCQs

Maths — AREAS RELATED TO CIRCLES

Frequently Asked Questions

Q 01 What is meant by a circle in geometry?

Q 02 What is the area of a circle?

Q 03 What does \(\pi\) represent in circle formulas?

Q 04 Define a sector of a circle.

Q 05 What is a minor sector?

Q 06 What is a major sector?

Q 07 How is the area of a sector calculated?

Q 08 Why is the angle at the centre important in sector problems?

Q 09 What is a segment of a circle?

Q 10 What is a minor segment?

Q 11 What is a major segment?

Q 12 How do you find the area of a minor segment?

Q 13 How is the area of a major segment obtained?

Q 14 Why are triangles used while finding the area of a segment?

Q 15 What is a chord of a circle?

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