Area of Sectors
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Question 1 of 5
1. Question
Find the area of the sector
Round your answer to `2` decimal placesUse `pi=3.141592654`- `\text(Area )=` (190.85, 190.76, 190.93)`\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)=9``theta=270°`Recall that a circle measures `360°`List the value of `theta` as a fraction of the circle$$\frac{\color{#007DDC}{\theta}}{360°}$$ `=` $$\frac{\color{#007DDC}{270°}}{360°}$$ `=` `3/4` Simplified Next, multiply `3/4` to the area of a circle formulaUse `pi=3.141592654` See `pi` explained`\text(Area)` `=` `3/4``times pi times``\text(radius)^2` `=` `3/4`` times pi times``\text(9)^2` Plug in the known values `=` `3/4 times pi times 81` Evaluate `=` `190.85175` `=` `190.85 \text(cm)^2` Rounded to two decimal places The given measurements are in centimetres, so the area is measured as square centimetres`\text(Area)=190.85 \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` `190.85 cm^2` `pi=3.14` `190.76 cm^2` `pi=(22)/(7)` `190.93 cm^2` -
Question 2 of 5
2. Question
Find the area of the sector
Round your answer to `2` decimal placesUse `pi=3.141592654`- `\text(Area )=` (26.94, 26.93, 26.95)`\text(m)^2`
Correct
Keep Going!
Incorrect
Area of a Sector Formula
$$\text{Area}=\frac{\color{#007DDC}{\theta}}{360°}\times \pi \times \color{#e65021}{r}^2$$Given Lengths
`\text(radius)=10.5``theta=28°`Solve for the area using the area of a sector formulaUse `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 `=` $$\frac{\color{#007DDC}{28°}}{360°}\times \pi \times \color{#e65021}{10.5}^2$$ Plug in the known values `=` `0.07777 times pi times 110.25` Evaluate `=` `26.93915` `=` `26.94 \text(m)^2` Rounded to two decimal places The given measurements are in metres, so the area is measured as square metres`\text(Area)=26.94 \text(m)^2`The answer will depend on which `pi` you use.In this solution we used: `pi=3.141592654`.Using Answer `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
3. Question
Find the area of the sector
Round your answer to `2` decimal placesUse `pi=3.141592654`- `\text(Area )=` (544.73, 544.46, 544.95)`\text(cm)^2`
Correct
Excellent!
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 formulaUse `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
4. Question
Find the area of the sector
Round your answer to `2` decimal placesUse `pi=3.141592654`- `\text(Area )=` (1202.64, 1202.03, 1203.13)`\text(cm)^2`
Correct
Well Done!
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 formulaUse `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
5. Question
Find the area of the larger sector
Round your answer to `2` decimal placesUse `pi=3.141592654`- `\text(Area )=` (1698.97, 1698.11, 1699.66)`\text(cm)^2`
Hint
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Exceptional!
Incorrect
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 formulaUse `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`