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Question 1 of 4
Find the area of the Circle
Round your answer to `1` decimal place
Use `pi=3.141592654`
Incorrect
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Given Lengths
`\text(diameter)=18`
First, find the radius of the circle. Note that the radius is half of the diameter.
`\text(radius)` |
`=` |
$$\frac{\color{#00880a}{\text{diameter}}}{2}$$ |
|
|
`=` |
$$\frac{\color{#00880a}{\text{18}}}{2}$$ |
|
`\text(radius)` |
`=` |
`9` |
Finally, solve for the area using the formula: `A=pi``r^2`
`\text(Area)` |
`=` |
`pi times``\text(radius)^2` |
Area of a Circle Formula |
|
`=` |
`3.141592654 times ``9^2` |
Plug in the known values |
|
`=` |
`3.141592654 times 81` |
Evaluate |
|
`=` |
`254.46900` |
|
`=` |
`254.5 mm^2` |
Rounded to `1` decimal place |
The given measurements are in millimetres, so the area is measured as square millimetres
`\text(Area)=254.5 mm^2`
The answer will depend on which `pi` you use.
In this solution we used: `pi=3.141592654`.
`pi=3.141592654` |
`254.5 mm^2` |
`pi=3.14` |
`254.3 mm^2` |
`pi=(22)/(7)` |
`254.6 mm^2` |
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Question 2 of 4
Find the area of the Circle
Round your answer to `1` decimal place
Use `pi=3.14`
Incorrect
Given Lengths
`\text(diameter)=24`
First, find the radius of the circle. Note that the radius is half of the diameter
`\text(radius)` |
`=` |
$$\frac{\color{#00880a}{\text{diameter}}}{2}$$ |
|
|
`=` |
$$\frac{\color{#00880a}{\text{24}}}{2}$$ |
|
`\text(radius)` |
`=` |
`12` |
Finally, solve for the area using the formula: `A=pi``r^2`
`\text(Area)` |
`=` |
`pi times``\text(radius)^2` |
Area of a Circle Formula |
|
`=` |
`3.14 times ``12^2` |
Plug in the known values |
|
`=` |
`3.14 times 144` |
Evaluate |
|
`=` |
`452.16` |
|
`=` |
`452.2 m^2` |
Rounded to `1` decimal place |
The given measurements are in metres, so the area is measured as square metres
`\text(Area)=452.2 m^2`
The answer will depend on which `pi` you use.
In this solution we used: `pi=3.14`.
`pi=3.14` |
`452.2 m^2` |
`pi=3.141592654` |
`452.4 m^2` |
`pi=(22)/(7)` |
`452.6 m^2` |
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Question 3 of 4
Find the area of the Circle
Round your answer to `1` decimal place
Use `pi=3.14`
Incorrect
Given Lengths
`\text(diameter)=4`
First, find the radius of the circle
Note that the radius is half of the diameter
`\text(radius)` |
`=` |
$$\frac{\color{#00880a}{\text{diameter}}}{2}$$ |
|
|
`=` |
$$\frac{\color{#00880a}{\text{4}}}{2}$$ |
|
`\text(radius)` |
`=` |
`2` |
Finally, solve for the area using the formula: `A=pi``r^2`
`\text(Area)` |
`=` |
`pi times``\text(radius)^2` |
Area of a Circle Formula |
|
`=` |
`3.14 times ``2^2` |
Plug in the known values |
|
`=` |
`3.14 times 4` |
Evaluate |
|
`=` |
`12.56` |
|
`=` |
`12.6 cm^2` |
Rounded to `1` decimal place |
The given measurements are in centimetres, so the area is measured as square centimetres
`\text(Area)=12.6 cm^2`
The answer will depend on which `pi` you use.
In this solution we used: `pi=3.14`.
`pi=3.14` |
`12.6 cm^2` |
`pi=3.141592654` |
`12.6 cm^2` |
`pi=(22)/(7)` |
`12.6 cm^2` |
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Question 4 of 4
Find the area of the yellow-shaded region.
Round your answer to `2` decimal places
Use `pi=3.141592654`
Incorrect
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Given Lengths
`\text(radius)` (Larger Semicircle)`=7`
`\text(diameter)` (Smaller Semicircle)`=7`
First, solve for the area of the Larger Semicircle
`\text(Area)``\text(Larger Semicircle)` |
`=` |
`1/2 xx pi xx``\text(radius)^2` |
|
`=` |
`1/2 xx 3.141592654 xx``7^2` |
`\text(Area)` |
`=` |
`76.96902 m^2` |
We can see on the image that the diameter of the Smaller Semicircle is `7`
We will use that to solve for the radius of the Smaller Semicircle, which is half of its diameter
`\text(radius)``\text(Smaller Semicircle)` |
`=` |
$$\frac{\color{#00880a}{\text{diameter}}}{2}$$ |
|
`=` |
$$\frac{\color{#00880a}{\text{7}}}{2}$$ |
|
`=` |
`3.5 m` |
Next, find the area of the Smaller Semicircle
`\text(Area)``\text(Smaller Semicircle)` |
`=` |
`1/2 xx pi xx``\text(radius)^2` |
|
`=` |
`1/2 xx 3.141592654 times ``3.5^2` |
`\text(Area)` |
`=` |
`19.24225 m^2` |
Finally, add the area of the Larger Semicircle and the area of the Smaller Semicircle
`\text(Final Area)` |
`=` |
`76.96902``+``19.24225` |
|
`=` |
`96.21127` |
|
`=` |
`96.21 m^2` |
Rounded to `2` decimal places |
The given measurements are in metres, so the area is measured as square metres
`\text(Area)=96.21 m^2`
The answer will depend on which `pi` you use.
In this solution we used: `pi=3.141592654`.
`pi=3.141592654` |
`96.21 m^2` |
`pi=3.14` |
`96.16 m^2` |
`pi=(22)/(7)` |
`96.25 m^2` |