Circle: Circumference and Area Applications → Lesson

Lesson – Circle

The Circle

- Centre, O and radius r.
- Set of points r distance from centre O.
- Chord is a segment with endpoints on circle.
- Diameter is the chord that contains centre.
- Diameter length is twice radius.
- Tangent intersects circle at exactly one point called point of tangency.
- Tangent is perpendicular to radius.
- Circumference C=2πr=πd
- $$ Area,~ A={πr^2}=\frac{1}{4}{ πd^2}$$
- $$Arc\hspace{1mm} Length\hspace{1mm} is\hspace{1mm}\frac{ θ}{360} C$$
- $$Sector\hspace{1mm} Area\hspace{1mm} is\hspace{1mm}\frac{ θ}{360} A$$

Irrational Number π

The ratio of circumference to diameter is equal to

$$π=\frac{Circumference}{Diameter}≈\frac{22}{7}≈3.14$$

Q1.

Find the circumference of a circle whose radius is 14 cm. Round your answer to nearest tens of centimeter.

a.	90	b.	80
c.	70	d.	60

$$\frac{C}{2r}=\frac{22}{7}$$

$$C=\frac{22}{7}×2×14=88$$

Irrational Number π

$$Area=πr^2$$

$$Remember: π≈\frac{22}{7}$$

Q2.

Find the area of a circle whose radius is 7 cm. Round your answer to 3 s.f.

a.	147	b.	168
c.	154	d.	161

$$A=\frac{22}{7}×7^2$$

$$C=\frac{22}{7}=154$$

Circle: Area and Circumference
	$$Circumference C=2πr=πd$$	$$Area, A=πr^2=\frac{1}{4} πd^2$$
Q3.	Can circumference of a circle be greater than its area? Justify your answer.
	$$2πr> πr^2$$	$$2> r$

$$Circle: Area and Circumference$$

$$Circumference C=2πr=πd$$

$$Area, A=πr^2=\frac{1}{4} πd^2$$

Q4.

$$Complete the following table.$$

$$Radius$$	$$Circumference$$	$$Area$$
$$0.1$$	$$0.2π=0.628$$	$$0.01π=0.0314$$
$$\frac{1}{2}$$	$$π$$	$$\frac{4}{π}$$
$$1$$	$$π$$	$$π$$

Circle: Relate Expressions

Q5.

A semicircle has radius and a circle has radius Find the relation between and if the perimeter of semicircle is equal to the circumference of the circle.