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Assertion & Reason Test: Areas Related to Circles - Class 10 MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 10 - Assertion & Reason Test: Areas Related to Circles

Assertion & Reason Test: Areas Related to Circles for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Assertion & Reason Test: Areas Related to Circles questions and answers have been prepared according to the Class 10 exam syllabus.The Assertion & Reason Test: Areas Related to Circles MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Assertion & Reason Test: Areas Related to Circles below.
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Assertion & Reason Test: Areas Related to Circles - Question 1

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : In a circle of radius 6 cm, the angle of a sector 60o. Then the area of the sector is 186/7 cm2.

Reason: Area of the circle with radius r is πr2.

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 1
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Area of the sector = θ/360 x πr2

= 60/360 x 22/7 x 6 x 6

= 132/7 = 186/7cm2.

Assertion & Reason Test: Areas Related to Circles - Question 2

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.

Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πr

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 2
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Area swept by minute hand in 5 minutes

(Angle in 5 minutes by minute hand is 30o)

Assertion & Reason Test: Areas Related to Circles - Question 3

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : If the outer and inner diameter of a circular path is 10 m and 6 m then area of the path is 16π m2.

Reason : If R and r be the radius of outer and inner circular path = π(R2 -r2).

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 3
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both assertion and reason are correct. Also, Reason is the correct explanation of the assertion.

Area of the path

Assertion & Reason Test: Areas Related to Circles - Question 4

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : If a wire of length 22 cm is bent in the shape of a circle, then area of the circle so formed is 40 cm2.

Reason : Circumference of the circle = length of the wire.

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 4
Assertion (A) is false but reason (R) is true. Assertion is not correct, but the reason is true.

2π r = 22

r = 3.5 cm

Area of the circle = 22/7 x 3.5 x 3.5 = 38.5 cm2

Assertion & Reason Test: Areas Related to Circles - Question 5

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : If the circumference of two circles are in the ratio 2 : 3 then ratio of their areas is 4 : 9.

Reason : The circumference of a circle of radius r is 2πr and its area is πr2.

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 5
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Given,

Now, ratio of their areas be

Also, circumference of circle = 2πr.

Assertion & Reason Test: Areas Related to Circles - Question 6

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.

Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 6
In the case of assertion

Let r1 = 24 cm and r2 = 7 cm

Area of first circle = πr12 = π(24)2 = 576π cm2

Area of second circle = πr22 =π(7)2 = 49π cm2

According to question,

Area of circle = Area of first circle + Area of second circle

πR2 = 576π +49π

[where, R be radius of circle]

R2 = 625 =25 cm

Diameter of a circle = 2R = 2 × 25 = 50 cm.

∴ Assertion is correct.

In case of reason:

Let the radius of the circle be r.

Circumference of circle = 2πr

Area of circle = πr2

Given that, the circumference of the circle and the area of the circle are equal. This implies, 2πr = pπ2

r = 2

Therefore, the radius of the circle is 2 units.

∴ Reason is correct.

Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.

Assertion & Reason Test: Areas Related to Circles - Question 7

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): In covering a distance s meter, a circular wheel of radius r meter makes s/2πr revolution.

Reason (R): The distance travelled by a circular wheel of diameter d cm in one revolution is 2πd cm.

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 7
In case of assertion

The distance covered in one revolution is 2πr, that is, its circumference.

∴ Assertion is correct

In case of reason:

Because the distance travelled by the wheel in one revolution is equal to its circumference Circumference of wheel = π × diameter

= π × d

= πd

Hence the given answer in the question is incorrect.

∴ Reason is incorrect.

Hence, assertion is correct and reason is incorrect.

Assertion & Reason Test: Areas Related to Circles - Question 8

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): If circumferences of two circles are equal, then their areas will be equal.

Reason (R): If the areas of two circles are equal, then their circumferences are equal.

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 8
In case of assertion: If circumferences of two circles are equal, then their corresponding radii are equal. So, their areas will be equal.

∴ Assertion is correct.

In case of reason:

If areas of two circles are equal, then their corresponding radii are equal. So, their circumference will be equal.

∴ Reason is correct.

Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.

Assertion & Reason Test: Areas Related to Circles - Question 9

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : If the circumference of a circle is 176 cm, then its radius is 28 cm.

Reason : Circumference = 2π x radius

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 9
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both assertion and reason are correct. Also Reason is the correct explanation of the assertion.

Assertion & Reason Test: Areas Related to Circles - Question 10

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion: A wire is looped in the form of a circle of radius 28 cm. It is bent into a square. Then the area of the square is 1936 cm2.

Reason : Angle described by a minute hand in 60 minutes = 360o.

Detailed Solution for Assertion & Reason Test: Areas Related to Circles - Question 10

Assertion (A) is false but reason (R) is true.

We have,

2π r = length of wire

2 x 22/7 x 28 = length of wire

length of wire = 176cm

Now, perimeter of square = 176

4a = 176

a = 44

Area of square = (44)2 = 1936 cm2
The minute hand moves 360 degrees in 60 minute(or 6 degrees in one minute) and hour hand moves 360 degrees in 12 hours(or 0.5 degrees in 1 minute).

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