Mathematics Multiple Choice Questions & Answers 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
Answer: b
Clarification: 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
Answer: c
Clarification: 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
Answer: a
Clarification: 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
Answer: b
Clarification: 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 {2pi r}{2})
b) (frac {2pi r}{2})
c) (frac {pi r}{2})
d) (frac {pi r^2}{2})
Answer: d
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: a
Clarification: 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
Answer: d
Clarification: 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
Answer: c
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: d
Clarification: 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