# Class 10 Maths MCQ – Areas Related to Circles

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

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 = πd2
b) A = πs2
c) A = πr2
d) A = πa2

Explanation: The area of a circle (A) = πr2.
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

Explanation: The area of a circle (A) = πr2
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

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) $$\frac {\pi r^2}{2}$$

Explanation: A semicircle is half of a full circle. Hence, the area of a semicircle is also half of a circle. Half of πr2 is $$\frac {\pi r^2}{2}$$. Therefore, the area of a semicircle is $$\frac {\pi r^2}{2}$$.
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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

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

Explanation: The area of the semicircle = πr2/2
= ($$\frac {22}{7}$$ × 62)/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

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

Explanation: The area of the circle (A) = πr2
2 = $$\frac {22}{7}$$ × r2
r2 = $$\frac {7}{22}$$ × 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

Explanation: The area of the circle (A) = πr2
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

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

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

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

Explanation: The area of the circle (A) = πr2
6 = $$\frac {22}{7}$$ × r2
r2 = 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

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

More MCQs on Class 10 Maths Chapter 12:

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