Area and circumference of a circle

Q: What are the formulas for the area and circumference of a circle?

Area = \pi r^2 and circumference = 2\pi r.

Q: Which value of π should I use?

Use \tfrac{22}{7} when the radius is a multiple of 7, and 3.14 otherwise. Use whichever the question tells you.

Q: How do you find the area of a semicircle?

Half of the circle's area: \tfrac{1}{2}\pi r^2. Its perimeter is \pi r + 2r, because it includes the straight edge.

The circumference is the distance around a circle and the area is the space inside it. Both depend on the radius (the distance from the centre to the edge). The diameter is twice the radius.

Formulas

Circumference

C = 2 π r = π d

Area

A = π r^{2}

Value of π to use

π \approx \frac{22}{7} or 3.14

Worked examples

Example 1. A circle has a radius of 7 cm. Find its circumference and area (take

π = \frac{22}{7}

$C = 2 \times \frac{22}{7} \times 7 = 44$ .
$A = \frac{22}{7} \times 7 \times 7 = 154$ .

Answer:

C = 44 cm, A = 154 cm^{2}

Example 2. A circular table has a diameter of 20 cm. Find its area (take

π = 3.14

Radius = $20 \div 2 = 10$ .
$A = 3.14 \times 1 0^{2} = 314$ .

Answer:

314 cm^{2}

Example 3. The area of a circle is

616 cm^{2}

. Find its radius (take

π = \frac{22}{7}

$\frac{22}{7} r^{2} = 616, so r^{2} = 616 \times \frac{7}{22} = 196$ .
$r = 196 = 14$ .

Answer: 14 cm

Common mistakes

Putting the diameter into $π r^{2}$ . Halve the diameter to get the radius first.
Squaring $π r$ instead of only $r$ . In $π r^{2}$ only the radius is squared.
Mixing up the two: circumference is a length (cm), area is in square units $(cm^{2})$ .

Practice questions with answers

1. The circumference of a circle is given by which formula? (r = radius, d = diameter)

A2*π*r
B $p i * r^{2}$
Cπ*r
D $p i * d^{2}$

Show answer

Answer: A) 2*π*r

Circumference

C = 2

*π*

r

= π*d. (π*

r^{2}

is the area.)

2. What is the formula for the area of a circle of radius r?

A $p i * r^{2}$
B2*π*r
Cπ*d
D $\frac{π r ^{2}}{2}$

Show answer

Answer: A)

p i * r^{2}

The area of a circle is given by

A

= π*

r^{2}

, while 2*π*

r

is its circumference.

3. What is the area of a circle with a diameter of 14 cm? (Take π =

\frac{22}{7}

)

A $154 cm^{2}$
B $196 cm^{2}$
C $88 cm^{2}$
D $308 cm^{2}$

Show answer

Answer: A)

154 cm^{2}

The radius is half the diameter, so

r = 7

cm. The area is π *

7^{2} = 49 * \frac{22}{7} = 154 cm^{2}

4. A wheel of radius 35 cm rotates 200 times per minute while a vehicle moves steadily.
What distance (in metres) does the vehicle travel in one minute? (Take π =

\frac{22}{7}

)

A395
B880
C485
D440

Show answer

Answer: D) 440

One turn

= 2 * \frac{22}{7} * 35 = 220

cm = 2.2 m. Distance = 200*2.2 = 440 m per minute.

5. The minute hand of a wall clock is 7 cm long.
In one full hour the tip sweeps out a complete circle.
Find the area swept by the minute hand in one hour. (Take π =

\frac{22}{7}

)

A $154 cm^{2}$
B $44 cm^{2}$
C $77 cm^{2}$
D $308 cm^{2}$

Show answer

Answer: A)

154 cm^{2}

In one hour the hand makes a full circle of radius 7 cm. Area =

\frac{22}{7} * 7 \times 7 = 154 cm^{2}

6. A quadrant-shaped glass pane has radius 35 cm. Find the length of beading needed to run all round its edge. (Take π =

\frac{22}{7}

)

A55 cm
B125 cm
C90 cm
D220 cm

Show answer

Answer: B) 125 cm

A quadrant is bounded by an arc and two radii. Arc =

\frac{1}{4} * 2 * \frac{22}{7} * 35 = \frac{1}{4} * 220 = 55

cm. Beading = 55 + 35 + 35 = 125 cm. Answering 55 covers only the curve, 90 adds one radius instead of two, and 220 is the whole circumference.

Practise 200+ questions free →

10 free questions a day without an account — unlimited with a free account.

Practice by class

Frequently asked questions

What are the formulas for the area and circumference of a circle?

Area $= π r^{2}$ and circumference $= 2 π r$ .

Which value of π should I use?

Use $\frac{22}{7}$ when the radius is a multiple of 7, and 3.14 otherwise. Use whichever the question tells you.

How do you find the area of a semicircle?

Half of the circle's area: $\frac{1}{2} π r^{2}$ . Its perimeter is $π r + 2 r$ , because it includes the straight edge.

What is the difference between radius and diameter?

The radius runs from the centre to the edge. The diameter passes through the centre from edge to edge, so $d = 2 r$ .

Area and circumference of a circle

Formulas

Worked examples

Common mistakes

Practice questions with answers

Practice by class

Frequently asked questions

Related topics