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

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

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

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