Area of Sectors

Question 1 of 5

Find the area of the sector

Round your answer to

2

$2$ decimal places

Use

π = 3.141592654

$pi=3.141592654$

$Area =$ $\text(Area )=$ (190.85, 190.76, 190.93) ${cm}^{2}$ $\text(cm)^2$

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Area of a Sector Formula

Area = \frac{θ}{360 °} \times π \times r^{2}

$\text{Area}=\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$

Given Lengths

radius = 9

$\text(radius)=9$

θ = 270 °

$theta=270°$

Recall that a circle measures

360 °

$360°$

List the value of $θ$ $theta$ as a fraction of the circle

$\frac{\color{#007DDC}{\theta}}{360°}$	$=$ $=$	$\frac{\color{#007DDC}{270°}}{360°}$

	$=$ $=$	$\frac{3}{4}$ $3/4$	Simplified

Next, multiply $\frac{3}{4}$ $3/4$ to the area of a circle formula

Use

π = 3.141592654

$pi=3.141592654$ See

π

$pi$ explained

$Area$ $\text(Area)$	$=$ $=$	$\frac{3}{4}$ $3/4$ $\times π \times$ $times pi times$ ${radius}^{2}$ $\text(radius)^2$

	$=$ $=$	$\frac{3}{4}$ $3/4$ $\times π \times$ $times pi times$ $9^{2}$ $\text(9)^2$	Plug in the known values

	$=$ $=$	$\frac{3}{4} \times π \times 81$ $3/4 times pi times 81$	Evaluate

	$=$ $=$	$190.85175$ $190.85175$
	$=$ $=$	$190.85 {cm}^{2}$ $190.85 \text(cm)^2$	Rounded to two decimal places

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

Area = 190.85 {cm}^{2}

$\text(Area)=190.85 \text(cm)^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.141592654

$pi=3.141592654$ .

Using	Answer
$π = 3.141592654$ $pi=3.141592654$	$190.85 c m^{2}$ $190.85 cm^2$
$π = 3.14$ $pi=3.14$	$190.76 c m^{2}$ $190.76 cm^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$190.93 c m^{2}$ $190.93 cm^2$

Question 2 of 5

Find the area of the sector

Round your answer to

2

$2$ decimal places

Use

π = 3.141592654

$pi=3.141592654$

$Area =$ $\text(Area )=$ (26.94, 26.93, 26.95) $m^{2}$ $\text(m)^2$

Incorrect

Area of a Sector Formula

Area = \frac{θ}{360 °} \times π \times r^{2}

$\text{Area}=\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$

Given Lengths

radius = 10.5

$\text(radius)=10.5$

θ = 28 °

$theta=28°$

Solve for the area using the area of a sector formula

Use

π = 3.141592654

$pi=3.141592654$ See

π

$pi$ explained

$Area$ $\text(Area)$	$=$ $=$	$\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$	Area of a sector formula

	$=$ $=$	$\frac{\color{#007DDC}{28°}}{360°}\times \pi \times \color{#e65021}{10.5}^2$	Plug in the known values

	$=$ $=$	$0.07777 \times π \times 110.25$ $0.07777 times pi times 110.25$	Evaluate
	$=$ $=$	$26.93915$ $26.93915$
	$=$ $=$	$26.94 m^{2}$ $26.94 \text(m)^2$	Rounded to two decimal places

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

Area = 26.94 m^{2}

$\text(Area)=26.94 \text(m)^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.141592654

$pi=3.141592654$ .

Using	Answer
$π = 3.141592654$ $pi=3.141592654$	$26.94 m^2$
$pi=3.14$	$26.93 m^2$
$pi=(22)/(7)$	$26.95 m^2$

Question 3 of 5

Find the area of the sector

Round your answer to

$2$ decimal places

Use

$pi=3.141592654$

$\text(Area )=$ (544.73, 544.46, 544.95) $\text(cm)^2$

Incorrect

Area of a Sector Formula

$\text{Area}=\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$

Given Lengths

$\text(radius)=23$

$theta=118°$

Solve for the area using the area of a sector formula

Use

$pi=3.141592654$ See

$pi$ explained

$\text(Area)$	$=$	$\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$	Area of a sector formula

	$=$	$\frac{\color{#007DDC}{118°}}{360°}\times \pi \times \color{#e65021}{23}^2$	Plug in the known values

	$=$	$0.32777 times pi times 529$	Evaluate
	$=$	$544.73471$
	$=$	$544.73 \text(cm)^2$	Rounded to two decimal places

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

$\text(Area)=544.73 \text(cm)^2$

The answer will depend on which

$pi$ you use.

In this solution we used:

$pi=3.141592654$ .

Using	Answer
$pi=3.141592654$	$544.73 cm^2$
$pi=3.14$	$544.46 cm^2$
$pi=(22)/(7)$	$544.95 cm^2$

Question 4 of 5

Find the area of the sector

Round your answer to

$2$ decimal places

Use

$pi=3.141592654$

$\text(Area )=$ (1202.64, 1202.03, 1203.13) $\text(cm)^2$

Incorrect

Area of a Sector Formula

$\text{Area}=\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$

Given Lengths

$\text(radius)=37.5$

$theta=98°$

Solve for the area using the area of a sector formula

Use

$pi=3.141592654$ See

$pi$ explained

$\text(Area)$	$=$	$\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$	Area of a sector formula

	$=$	$\frac{\color{#007DDC}{98°}}{360°}\times \pi \times \color{#e65021}{37.5}^2$	Plug in the known values

	$=$	$0.27222222 times pi times 1406.25$	Evaluate
	$=$	$1202.64093$
	$=$	$1202.64 \text(cm)^2$	Rounded to two decimal places

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

$\text(Area)=1202.64 \text(cm)^2$

The answer will depend on which

$pi$ you use.

In this solution we used:

$pi=3.141592654$ .

Using	Answer
$pi=3.141592654$	$1202.64 cm^2$
$pi=3.14$	$1202.03 cm^2$
$pi=(22)/(7)$	$1203.13 cm^2$

Question 5 of 5

Find the area of the larger sector

Round your answer to

$2$ decimal places

Use

$pi=3.141592654$

$\text(Area )=$ (1698.97, 1698.11, 1699.66) $\text(cm)^2$

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Area of a Sector Formula

$\text{Area}=\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$

Given Lengths

$\text(radius)=26$

Recall that a circle measures

$360°$

Find the value of

$theta$ by subtracting the value of the smaller sector from

$360°$

$theta$	$=$	$360-72$

	$=$	$288°$

Next, solve for the area using the area of a sector formula

Use

$pi=3.141592654$ See

$pi$ explained

$\text(Area)$	$=$	$\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$	Area of a sector formula

	$=$	$\frac{\color{#007DDC}{288°}}{360°}\times \pi \times \color{#e65021}{26}^2$	Plug in the known values

	$=$	$0.8 times pi times 676$	Evaluate
	$=$	$1698.97330$
	$=$	$1698.97 \text(cm)^2$	Rounded to two decimal places

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

$\text(Area)=1698.97 \text(cm)^2$

The answer will depend on which

$pi$ you use.

In this solution we used:

$pi=3.141592654$ .

Using	Answer
$pi=3.141592654$	$1698.97 cm^2$
$pi=3.14$	$1698.11 cm^2$
$pi=(22)/(7)$	$1699.66 cm^2$

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Quiz summary

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1. Question

Hint

Great Work!

Area of a Sector Formula

Given Lengths

2. Question

Keep Going!

Area of a Sector Formula

Given Lengths

3. Question

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Area of a Sector Formula

Given Lengths

4. Question

Well Done!

Area of a Sector Formula

Given Lengths

5. Question

Hint

Exceptional!

Area of a Sector Formula

Given Lengths

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