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
View Answer

Answer: b
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 \(\frac {22}{7}\).
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2. What is the formula for the area of a circle?
a) A = πd2
b) A = πs2
c) A = πr2
d) A = πa2
View Answer

Answer: c
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
View Answer

Answer: a
Explanation: The area of a circle (A) = πr2
A = \(\frac {22}{7}\) × (3.14)2
A = 30.98 cm
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4. The perimeter of a circle is also called the circumference.
a) False
b) True
View Answer

Answer: b
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

Answer: d
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
View Answer

Answer: c
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

Answer: b
Explanation: The area of the semicircle = πr2/2
= (\(\frac {22}{7}\) × 62)/2
= 56.54 m
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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

Answer: a
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

Answer: c
Explanation: The area of the circle (A) = πr2
2 = \(\frac {22}{7}\) × r2
r2 = \(\frac {7}{22}\) × 2
r = √0.63 m
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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

Answer: a
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
View Answer

Answer: d
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

Answer: c
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

Answer: c
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

Answer: b
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
View Answer

Answer: d
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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter