# Mathematics Questions and Answers – Perimeter and Area of a Circle

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Perimeter and Area of a Circle”.

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

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

Sanfoundry Global Education & Learning Series – Mathematics – Class 10.

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