# The measurements of a circle(Circumferance, Area of a circle and a sector, Perimeter of a sector

## Circles

**In this hub we are going to be**

**looking at the different parts of a**

**circle and how to calculate each **

**of them. **

**The Circumference of a Circle, **

**this is the perimeter of a circle.**

**The Diameter = 2 radii **

**(twice the radius)**

**The Radius is half **

**the Diameter**

## PERIMETER of a Circle

**The formula for the circumference **

**of a Circle is;**

** C = TT D C = 2 TT r **

**(C = TT x D ) ( C = 2 x TT x r) **

**The Pi (TT) = 3.141592654**

** (check this on a calculator)**

**(Pi is a special number used to**

** calculate ****distance and area **

** when dealing with a circle)**

** **

**Your told that the**__Diameter__is 12cm in the above diagram,

** and you have to find the Circumference to 1 decimal**

** place.**

** C = TT D**

** C = TT x 12 = 37.699... (use your calculator)**

** C = 37.7 (1 decimal place) ANSWER**

**2. If the diameter was 12cm that makes the Radius 6cm**

** So now we'll calculate the circumference of the same circle **

** using the Radius and you have to find the Circumference to **

** 1 decimal **

__place__.

** C = 2 TT r **

** C = 2 x TT x 6 = 37.699....(use your calculator)**

** C = 37.7 (1 decimal place) ANSWER**

## AREA of a Circle

**The Area of a Circle is represented by the formula;**

** A = TT r ^{2}**

^{}

**So using the Circle above as an example;**

**We know that the Radius is 6cm (½ the Diameter which is 12cm)**

** A = TT r ^{2}**

^{}

^{}

** **

** A = TT x 6 ^{2}**

^{}

^{}

** **

** ****A = 113.0973355**

** A = 113.1cm ^{2} ( 1 d. p.) ANSWER**

**The red marked part of the circle**

**is known as an Arc**

## PERIMETER of a Semi-Circle

**If the arc is a semi-circle our**

**formula will be C = ½ TT D**

**We are asked to find the Perimeter of this Semi-Circle correct to 1 decimal place, and we are told the Diameter is 6cm.**

**Now the Perimeter is made up of the Arc(marked with red arrow) **

**plus the ****Diameter. So it's two parts to find the Perimeter of this **

**Semi-Circle.**

** (i) C = ½ TT D (½ because it's a Semi-Circle)**

** C = ½ x TT x 6 (do this on your calculator)**

** C = 9.42477**

** (ii) Perimeter = 9.42477 + 6 = 15.42477**

** = 15.4 ( 1 d. p.) ANSWER**

## AREA of a Semi-Circle

**Here we are finding the Area of a Semi-Circle.**

**Using the example above we know our Diameter is 6cm**

**So the Radius will be 3cm (½ the Diameter)**

**To find the Area of a Semi-Circle we use the following formula;**

** A = ½ TT r ^{2}**

^{}

^{}

** A = ½ x TT x 3 ^{2}**

^{}

^{}

** A = 14.137166...**

** A = 14.1cm ^{2} ( 1 d.p.) ANSWER**

## PERIMETER of a Quadrant

**A Quadrant is a ¼ of a Circle.**

**If the arc is a Quadrant our**

**formula will be C = ¼ TT D**

**We are asked to find the Perimeter of this Quadrant correct to 1 decimal place, and we are told the Radius is 8cm.**

**The Diameter is twice the Radius;**

**Therefore the Diameter is 16cm**

**Now the Perimeter is made up of the Arc**

**plus the two Radii ( These need to be **

**added ****on at the end to the perimeter of**

**the Quadrant's ****arc ****to find the total Perimeter of the Quadrant****. **

**So it's two parts to find the Perimeter of **

**this ****Quadrant.**

** (i) C = ¼ TT D ( ¼ because its a Quadrant)**

** C = ¼ x TT x 16**

** C = 12.56637061 (Perimeter of the arc)**

** (ii) **** Perimeter of Arc + Radii + Radii**

** **

** Perimeter = 12.56637061 + 8 + 8 = 28.566.......**

** **

** = 28.6 ( 1 d. p.) ANSWER**

## AREA of a Quadrant

**Here we are finding the Area of a Quadrant.**

**Using the example above we know our Diameter is 16cm**

**So the Radius will be 8cm (½ the Diameter)**

**To find the Area of a Quadrant we use the following formula;**

** A = ¼ TT r ^{2 }(¼ as its a Quadrant)**

^{}

** A = ¼ x TT x 8 ^{2 }(use your calculator)**

** A = 50.2654......**

^{}

** A = 50.3 cm ^{2 }( 1 d.p.) ANSWER**

^{}

^{}

## PERIMETER of Three Quadrants

**This Quadrant is a ¾ of a Circle.**

**Our ****formula will be C = ¾ TT D**

**We are asked to find the Perimeter of this Quadrant correct to 1 decimal place, and we are told the Radius is 10m.**

**The Diameter is twice the Radius;**

** Therefore the Diameter is 20m**

**Now the Perimeter is made up of the Arc**

**plus the two Radii ( These need to be **

**added ****on at the end to the perimeter of**

**the Quadrant's ****arc ****to find the total Perimeter of this Quadrant****. **

**So it's two parts to find the Perimeter of **

**this ****Quadrant.**

** (i) C = ¾ TT D ( ¾ because its three Quadrants)**

** **

** C = ¾ x TT x 20**

** C = 47.1238898 (Perimeter of the arc)**

** (ii)** __Perimeter of Arc__ + __Radii __+ __Radii__

** Perimeter = 47.1238898 + 10 + 10 = 67.123...**

** = 67.1m (1 d.p.)**

## AREA of Three Quadrants

**Here we are finding the Area **

**of this Quadrant. It has a value **

**of three Quadrants = ¾**

**Using the example above we know our Diameter is 20m**

**So the Radius will be 10m (½ the Diameter)**

**To find the Area of this Quadrant we use the following formula;**

** A = ¾ TT r ^{2 }(¾ as its three Quadrants)**

** A = ¾ x TT x 10 ^{2 }(use your calculator)**

** A = 235.619....**

** A = 235.6m ^{2} ( 1 d.p.)**

## PERIMETER of a Sector

**Here we are finding the Perimeter**

**of a Sector, it has a value of **

**60 degrees.**

**We are asked to find the Perimeter of this Sector correct**

** to 2 decimal places, ****and we are told the Radius is 15m.**

**The Diameter is twice the Radius;**

** Therefore the Diameter is 30m**

**Now the Perimeter is made up of the Arc**

**plus the two Radii ( These need to be **

**added ****on at the end, to the perimeter of**

**the Sector's ****arc ****to find the total Perimeter of this Sector****. **

**So it's two parts to find the Perimeter of**

** this Sector****.**

**This time we need to look at the fact we're not dealing with a whole Circle.**

**In fact we're dealing with a**__Fraction,__

^{60} / _{360 }(60 degrees over the whole Circle)

**This is the Fraction part, so let's put this into our formula for Perimeter.**

** (i) C = ^{60} / _{360 }TT D**

** C = 60 / 360 x TT x 30 (use your calculator)**

** C = 15.70796... (Perimeter of the arc)**

** (ii) Perimeter of Arc + Radii + Radii**

** **

** Perimeter = 15.70796... + 15 + 15 = 45.707.....**

** = 45.71m ( 2 d.p's) ANSWER **

## AREA of a Sector

**Here we are finding the Area **

**of this Sector, it has a Fractional**

**value of ^{60} / _{360 }, to two decimal**

**places.**

_{}

**Using the example above we know our Diameter is 30m**

**So the Radius will be 15m (½ the Diameter)**

**To find the Area of this Sector we'll use the following formula;**

** A = ^{60} / _{360} TT r^{2}**

^{}

^{}

^{}

^{}

^{}

^{}

** A = ^{60} / _{360 }TT 15^{2 }(use your calculator)**

** A = 117.809......**

** A = 117.81 m ^{2 }( 2 d.p's.)**

_{}