Areas of Circles 1

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Geometry

Area

Area of Circles

Areas of Circles 1

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Question 1 of 5

1. Question
Find the area of the circle

Round your answer to $1$ decimal place

Use $pi=3.14$
- $\text(Area )=$ (78.5, 78.6) $cm^2$
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Area of a Circle Formula

$\text(Area)=pi times$ $\text(radius)^2$

Given Lengths

$\text(radius)=5$

Solve for the area using the formula: $A=pi$ $r^2$

Use $pi=3.14$ See $pi$ explained

$\text(Area)$ $=$ $pi times$ $\text(radius)^2$ Area of a Circle Formula

$=$ $3.14 times$ $5^2$ Plug in the known values

$=$ $3.14 times 25$ Evaluate

$=$ $78.5 cm^2$

The given measurements are in centimetres, so the area is measured as square centimetres

$\text(Area)=78.5 cm^2$

The answer will depend on which $pi$ you use.

In this solution we used: $pi=3.14$ .

Using Answer

$pi=3.14$ $78.5 cm^2$

$pi=3.141592654$ $78.5 cm^2$

$pi=(22)/(7)$ $78.6 cm^2$

Using	Answer
$pi=3.14$	$78.5 cm^2$
$pi=3.141592654$	$78.5 cm^2$
$pi=(22)/(7)$	$78.6 cm^2$

Question 2 of 5

Find the area of the circle

Round your answer to

$1$ decimal place

Use

$pi=3.14$

$\text(Area )=$ (346.2, 346.4, 346.5) $m^2$

Incorrect

Area of a Circle Formula

$\text(Area)=pi times$ $\text(radius)^2$

Given Lengths

$\text(diameter)=21$

First, find the radius of the circle. Note that the radius is half of the diameter

$\text(radius)$	$=$	$\frac{\color{#00880a}{\text{diameter}}}{2}$

	$=$	$\frac{\color{#00880a}{\text{21}}}{2}$

$\text(radius)$	$=$	$10.5$

Finally, solve for the area using the formula:

$A=pi$ $r^2$

Use

$pi=3.14$ See

$pi$ explained

$\text(Area)$	$=$	$pi times$ $\text(radius)^2$	Area of a Circle Formula
	$=$	$3.14 times$ $10.5^2$	Plug in the known values
	$=$	$3.14 times 110.25$	Evaluate
	$=$	$346.185$
	$=$	$346.2 m^2$	Rounded to $1$ decimal place

The given measurements are in metres, so the area is measured as square metres

$\text(Area)=346.2 m^2$

The answer will depend on which

$pi$ you use.

In this solution we used:

$pi=3.14$ .

Using	Answer
$pi=3.14$	$346.2 m^2$
$pi=3.141592654$	$346.4 m^2$
$pi=(22)/(7)$	$346.5 m^2$

Question 3 of 5

Find the area of the Circle

Round your answer to

$1$ decimal place

Use

$pi=3.14$

$\text(Area )=$ (149.5, 149.6) $km^2$

Incorrect

Area of a Circle Formula

$\text(Area)=pi times$ $\text(radius)^2$

Given Lengths

$\text(diameter)=13.8$

First, find the radius of the circle
Note that the radius is half of the diameter

$\text(radius)$	$=$	$\frac{\color{#00880a}{\text{diameter}}}{2}$

	$=$	$\frac{\color{#00880a}{\text{13.8}}}{2}$

$\text(radius)$	$=$	$6.9$

Finally, solve for the area using the formula:

$A=pi$ $r^2$

Use

$pi=3.14$ See

$pi$ explained

$\text(Area)$	$=$	$pi times$ $\text(radius)^2$	Area of a Circle Formula
	$=$	$3.14 times$ $6.9^2$	Plug in the known values
	$=$	$3.14 times 47.61$	Evaluate
	$=$	$149.4954$
	$=$	$149.5 km^2$	Rounded to $1$ decimal place

The given measurements are in kilometres, so the area is measured as square kilometres

$\text(Area)=149.5 km^2$

The answer will depend on which

$pi$ you use.

In this solution we used:

$pi=3.14$ .

Using	Answer
$pi=3.14$	$149.5 km^2$
$pi=3.141592654$	$149.6 km^2$
$pi=(22)/(7)$	$149.6 km^2$

Question 4 of 5

4. Question
Find the area of the orange-shaded region.

The given measurements are in centimetres.

Round your answer to $1$ decimal place.

$pi=3.14$
- $\text(Area )=$ (103.7, 103.6) $cm^2$
Hint

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Area of a Circle Formula

$\text(Area)=pi xx$ $\text(radius)^2$

Given Lengths

$\text(radius)$ (Whole Circle) $=7$

$\text(thickness)$ (Shaded Region) $=3$

First, solve for the area of the Whole Circle

Use $pi=3.14$ See $pi$ explained

$\text(Area)$ _{$\text(Whole Circle)$} $=$ $pi xx$ $\text(radius)^2$

$=$ $3.14 xx$ $7^2$

$\text(Area)$ $=$ $153.86 cm^2$

Find the radius of the Inner Circle by subtracting the thickness of the shaded region from the radius of the Whole Circle.

$\text(radius)$ _{$\text(Inner Circle)$} $=$ $\text(radius)$ $-$ $\text(thickness)$

$=$ $7$ $-$ $3$

$=$ $4 cm$

Next, find the area of the Inner Circle

$\text(Area)$ _{$\text(Inner Circle)$} $=$ $pi xx$ $\text(radius)^2$

$=$ $3.14 times$ $4^2$

$\text(Area)$ $=$ $50.24 cm^2$

Finally, subtract the area of the Inner Circle from the area of the Whole Circle

$\text(Final Area)$ $=$ $153.86$ $-$ $50.24$

$=$ $103.62$

$=$ $103.6 cm^2$ Rounded to $1$ decimal place

The given measurements are in centimetres, so the area is measured as square centimetres

$\text(Area)=103.6 cm^2$

The answer will depend on which $pi$ you use.

In this solution we used: $pi=3.14$ .

Using Answer

$pi=3.14$ $103.6 cm^2$

$pi=3.141592654$ $103.7 cm^2$

$pi=(22)/(7)$ $103.7 cm^2$
Question 5 of 5

5. Question
Find the area of the yellow-shaded region.

Round your answer to $1$ decimal place

Use $pi=3.14$
- $\text(Area )=$ (50.2, 50.3) $cm^2$
Hint

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Area of a Semicircle Formula

$\text(Area)=1/2 xx pi xx$ $\text(radius)^2$

Given Lengths

$\text(radius)$ (Whole Semicircle) $=9$

$\text(thickness)$ (Shaded Region) $=2$

First, solve for the area of the Whole Semicircle

Use $pi=3.14$ See $pi$ explained

$\text(Area)$ _{$\text(Whole Semicircle)$} $=$ $1/2 xx pi xx$ $\text(radius)^2$

$=$ $1/2 xx 3.14 xx$ $9^2$

$\text(Area)$ $=$ $127.17 cm^2$

Find the radius of the Inner Semicircle by subtracting the thickness of the shaded region from the radius of the Whole Semicircle.

$\text(radius)$ _{$\text(Inner Semicircle)$} $=$ $\text(radius)$ $-$ $\text(thickness)$

$=$ $9$ $-$ $2$

$=$ $7 cm$

Next, find the area of the Inner Semicircle

$\text(Area)$ _{$\text(Inner Semicircle)$} $=$ $1/2 xx pi xx$ $\text(radius)^2$

$=$ $1/2 xx 3.14 times$ $7^2$

$\text(Area)$ $=$ $76.93 cm^2$

Finally, subtract the area of the Inner Semicircle from the area of the Whole Semicircle

$\text(Final Area)$ $=$ $127.17$ $-$ $76.93$

$=$ $50.24$

$=$ $50.2 cm^2$ Rounded to $1$ decimal place

The given measurements are in centimetres, so the area is measured as square centimetres

$\text(Area)=50.2 cm^2$

The answer will depend on which $pi$ you use.

In this solution we used: $pi=3.14$ .

Using Answer

$pi=3.14$ $50.2 cm^2$

$pi=3.141592654$ $50.3 cm^2$

$pi=(22)/(7)$ $50.3 cm^2$

Areas of Circles 1

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Quiz summary

Information

1. Question

Hint

Well Done!

Area of a Circle Formula

Given Lengths

2. Question

Great Work!

Area of a Circle Formula

Given Lengths

3. Question

Keep Going!

Area of a Circle Formula

Given Lengths

4. Question

Hint

Correct!

Area of a Circle Formula

Given Lengths

5. Question

Hint

Fantastic!

Area of a Semicircle Formula

Given Lengths

Quizzes

$\text(Area)$ _{$\text(Whole Circle)$}	$=$	$pi xx$ $\text(radius)^2$
	$=$	$3.14 xx$ $7^2$
$\text(Area)$	$=$	$153.86 cm^2$

$\text(radius)$ _{$\text(Inner Circle)$}	$=$	$\text(radius)$ $-$ $\text(thickness)$
	$=$	$7$ $-$ $3$
	$=$	$4 cm$

$\text(Area)$ _{$\text(Inner Circle)$}	$=$	$pi xx$ $\text(radius)^2$
	$=$	$3.14 times$ $4^2$
$\text(Area)$	$=$	$50.24 cm^2$

$\text(Final Area)$	$=$	$153.86$ $-$ $50.24$
	$=$	$103.62$
	$=$	$103.6 cm^2$	Rounded to $1$ decimal place

$\text(Area)$ _{$\text(Whole Semicircle)$}	$=$	$1/2 xx pi xx$ $\text(radius)^2$
	$=$	$1/2 xx 3.14 xx$ $9^2$
$\text(Area)$	$=$	$127.17 cm^2$

$\text(radius)$ _{$\text(Inner Semicircle)$}	$=$	$\text(radius)$ $-$ $\text(thickness)$
	$=$	$9$ $-$ $2$
	$=$	$7 cm$

$\text(Area)$ _{$\text(Inner Semicircle)$}	$=$	$1/2 xx pi xx$ $\text(radius)^2$
	$=$	$1/2 xx 3.14 times$ $7^2$
$\text(Area)$	$=$	$76.93 cm^2$

$\text(Final Area)$	$=$	$127.17$ $-$ $76.93$
	$=$	$50.24$
	$=$	$50.2 cm^2$	Rounded to $1$ decimal place