This set of Class 10 Maths Chapter 12 Multiple Choice Questions & Answers (MCQs) focuses on “Areas Related to Circles”. These MCQs are created based on the latest CBSE syllabus and the NCERT curriculum, offering valuable assistance for exam preparation.

1. What is the formula for the circumference of a circle?

a) C = 2πd

b) C = 2πr

c) C = 2πa

d) C = 2πs

View Answer

Explanation: The circumference of a circle (C) = 2πr.

Where C is the circumference of the circle and r is the radius of the given circle.

The value of π is taken as \(\frac {22}{7}\).

2. What is the formula for the area of a circle?

a) A = πd^{2}

b) A = πs^{2}

c) A = πr^{2}

d) A = πa^{2}

View Answer

Explanation: The area of a circle (A) = πr

^{2}.

Where A is the area of the circle and r is the radius of the given circle.

The value of π is taken as \(\frac {22}{7}\).

3. Find the area of the circle if the radius is 3.14 cm.

a) 30.98 cm

b) 30.48 cm

c) 30.68 cm

d) 30.58 cm

View Answer

Explanation: The area of a circle (A) = πr

^{2}

A = \(\frac {22}{7}\) × (3.14)

^{2}

A = 30.98 cm

4. The perimeter of a circle is also called the circumference.

a) False

b) True

View Answer

Explanation: The path that surrounds the outline of a two-dimensional shape is called the perimeter. The perimeter of a circle is also called the circumference.

5. The area of a semicircle is _____

a) \(\frac {2\pi r}{2}\)

b) \(\frac {2\pi r}{2}\)

c) \(\frac {\pi r}{2}\)

d) \(\frac {\pi r^2}{2}\)

View Answer

Explanation: A semicircle is half of a full circle. Hence, the area of a semicircle is also half of a circle. Half of πr

^{2}is \(\frac {\pi r^2}{2}\). Therefore, the area of a semicircle is \(\frac {\pi r^2}{2}\).

6. What is the circumference of a circle if the radius is 7 m?

a) 8 m

b) 2 m

c) 44 m

d) 22 m

View Answer

Explanation: The circumference of a circle (C) = 2πr.

C = 2 × \(\frac {22}{7}\) × 7

C = 44 m

7. Find the area of a semicircle if the radius is 6 cm.

a) 1.35 m

b) 6.54 m

c) 18.00 m

d) 8.05 m

View Answer

Explanation: The area of the semicircle = πr

^{2}/2

= (\(\frac {22}{7}\) × 6

^{2})/2

= 56.54 m

8. Find the radius of the circle if the circumference is 12 m.

a) 1.90 m

b) 1.09 m

c) 7.90 m

d) 1.40 m

View Answer

Explanation: The circumference of a circle (C) = 2πr.

12 = 2 × \(\frac {22}{7}\) × r

r = \(\frac {12}{2} \times \frac {7}{22}\)

r = 1.90 m

9. Find the radius of a circle if 2 m is the area of the circle.

a) √0.83 m

b) 5 m

c) √0.63 m

d) √38 m

View Answer

Explanation: The area of the circle (A) = πr

^{2}

2 = \(\frac {22}{7}\) × r

^{2}

r

^{2}= \(\frac {7}{22}\) × 2

r = √0.63 m

10. Find the radius of the circle if the area of the circle is 22 cm.

a) 1521.14 m

b) 1511.14 m

c) 1021.14 m

d) 1520.14 m

View Answer

Explanation: The area of the circle (A) = πr

^{2}

A = \(\frac {22}{7}\) (22)

^{2}

A = 1521.14 m

11. What is the circumference of the circle if the radius is 121 cm?

a) 760.00 cm

b) 765.57 cm

c) 750.57 cm

d) 760.57 cm

View Answer

Explanation: The circumference of the circle (C) = 2πr

C = 2 × \(\frac {22}{7}\) × 121

A = 760.57 cm

12. Find the radius of the wheel if the wheel rotates 100 times to cover 500 m.

a) 0.07 m

b) 0.47 cm

c) 0.79 m

d) 0.57 cm

View Answer

Explanation: One rotation of the wheel = circumference of the wheel

100 rotations = 500 m

1 rotation = 5 m

So, circumference = 5 m

2πr = 5 m

r = 5 × \(\frac {7}{22} \times \frac {1}{2}\)

r = 0.79m

13. The difference between circumference and diameter of a ring is 10 cm. Find the radius of the ring.

a) 3.07 cm

b) 0.37 cm

c) 2.33 cm

d) 4.57 cm

View Answer

Explanation: Circumference – Diameter = 10 cm (∵ Diameter = 2 × radius)

2πr – 2r = 10 cm

2r(π – 1) = 10 cm

2r(\(\frac {22}{7}\) – 1) = 10 cm

2r(\(\frac {15}{7}\)) = 10 cm

r = 10 × \(\frac {7}{15} \times \frac {1}{2}\)

r = 2.33 cm

14. Find the diameter of the circle if the area of the circle is 6 m.

a) 3.07 m

b) 2.74 m

c) 2.33 m

d) 4.57 m

View Answer

Explanation: The area of the circle (A) = πr

^{2}

6 = \(\frac {22}{7}\) × r

^{2}

r

^{2}= 1.90

r = √1.90

r = 1.37 m

Diameter of the circle = 2 × radius

= 2 × 1.37

= 2.74 m

15. Find the diameter of the circle if the circumference of the circle is \(\frac {11}{5}\)m.

a) 23.07 cm

b) 20.74 cm

c) 72.33 cm

d) 70 cm

View Answer

Explanation: The circumference of the circle = \(\frac {11}{5}\)m

2πr = \(\frac {11}{5}\)m

πd = \(\frac {11}{5}\)m (∵ Diameter = 2 × radius)

d = \(\frac {11}{5} \times \frac {7}{22}\)m

d = 0.7 m

d = 0.7 × 100 cm

d = 70 cm

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