Volume of Shapes 3
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Question 1 of 7
1. Question
Find the volume of the HemisphereRound your answer to `1` decimal placeUse `pi=3.141592654` `\text(Volume )=` (41.2) `\text(m)^3`
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Volume of a Hemisphere
`\text(Volume)=1/2 times 4/3 times pi times``\text(radius)^3`Labelling the given lengths
`\text(radius)=2.7`Use the formula to find the volumeUse `pi=3.141592654` See `pi` explained`\text(Volume)` `=` `1/2 times 4/3 times pi times``\text(radius)^3` Volume of a Hemisphere formula `=` `1/2 times 4/3 times 3.141592654 times``2.7^3` Plug in the known lengths `=` `1/2 times 4/3 times 3.141592654 times 19.683` Simplify `=` `41.22397` `=` `41.2 \text(m)^3` Rounded to `1` decimal place The given measurements are in metres, so the volume is measured as metres cubed`\text(Volume)=41.2 \text(m)^3`The answer will depend on which `pi` you use.In this solution we used: `pi=3.141592654`.Using Answer `pi=3.141592654` `41.2 m^3` `pi=3.14` `41.2 m^3` `pi=(22)/(7)` `41.2 m^3` 
Question 2 of 7
2. Question
What is the volume of this cone?
Round your answer to `2` decimal placesUse `pi~~3.14` Volume`=` (287.83)`cm^3`
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Volume of a Cone
`V=1/3 xx pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))`Labelling the given lengths
`color(darkviolet)(\text(height)=11)``color(royalblue)(\text(radius)=5)`Use the formula to find the volume`pi~~3.14``V` `=` `1/3 xx pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))` Volume of a cone formula `=` `1/3 xx 3.14 xx color(royalblue)(5^2) xx color(darkviolet)(11)` Plug in the known lengths `=` `1/3 xx 3.14 xx 25 xx 11` Simplify `=` `287.83333` `=` `287.83 \ cm^3` Rounded to 2 decimal places The given measurements are in centimetres, so the volume is measured as centimetres cubedVolume`=287.83 \ cm^3` 
Question 3 of 7
3. Question
What is the volume of this sphere?
Round your answer to `2` decimal placesUse `pi~~3.14` Volume`=` (113.04)`mm^3`
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Volume of a Cone
`V=4/3 xx pi xx color(royalblue)(\text(radius)^3)`Labelling the given lengths
`color(royalblue)(\text(radius)=3)`Use the formula to find the volume`pi~~3.14``V` `=` `4/3 xx pi xx color(royalblue)(\text(radius)^3)` Volume of a sphere formula `=` `4/3 xx 3.14 xx color(royalblue)(3^3)` Plug in the known lengths `=` `4/3 xx 3.14 xx 27` Simplify `=` `113.04 \ mm^3` Rounded to 2 decimal places The given measurements are in millimetres, so the volume is measured as millimetres cubedVolume`=113.04 \ mm^3` 
Question 4 of 7
4. Question
Find the volume of the Pyramid `\text(Volume )=` (1456) `\text(m)^3`
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Volume of a Pyramid
`\text(Volume )=1/3 times``\text(length)``times``\text(width)``times``\text(height)`Labelling the given lengths
`\text(length)=21``\text(width)=8``\text(height)=26`First, find the area of the pyramid’s base, which is a rectangle`\text(Area)` `=` `\text(length)``times``\text(width)` Area of a Rectangle `=` `21``times``8` Plug in the known lengths `=` `168 \text(m)^2` Next, use the formula to find the volumeNote that `\text(area)``=``\text(length)``times``\text(width)``\text(Volume)` `=` `1/3 times``\text(length)``times``\text(width)``times``\text(height)` Volume of a Pyramid `=` `1/3 times``168``times``26` Plug in the known lengths `=` `1456 \text(m)^3` The given measurements are in metres, so the volume is measured as metres cubed`\text(Volume)=1456 \text(m)^3` 
Question 5 of 7
5. Question
Find the volume of the ConeRound your answer to the nearest whole numberUse `pi=3.141592654` `\text(Volume )=` (2545, 2543, 2546) `\text(cm)^3`
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Volume of a Cone
`\text(Volume)=1/3 times pi times``\text(radius)^2``times``\text(height)`Labelling the given lengths
`\text(radius)=9`Use the formula to find the volumeUse `pi=3.141592654` See `pi` explained`\text(Volume)` `=` `1/3 times pi times``\text(radius)^2``times``\text(height)` Volume of a Cone formula `=` `1/3 times 3.141592654 times``9^2``times``30` Plug in the known lengths `=` `1/3 times 3.141592654 times 81 times 30` Simplify `=` `2544.69` `=` `2545 \text(cm)^3` Rounded to the nearest whole number The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=2545 \text(cm)^3`The answer will depend on which `pi` you use.In this solution we used: `pi=3.141592654`.Using Answer `pi=3.141592654` `2545 cm^3` `pi=3.14` `2543 cm^3` `pi=(22)/(7)` `2546 cm^3` 
Question 6 of 7
6. Question
What is the volume of this cylinder?
Round your answer to `2` decimal placesUse `pi~~3.14` Volume`=` (1808.64)`m^3`
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Volume of a Cylinder
`V=pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))`Labelling the given lengths
`color(darkviolet)(\text(height)=13)``color(royalblue)(\text(radius)=8)`Use the formula to find the volume`pi~~3.14``V` `=` `pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))` Volume of a cylinder formula `=` `3.14 xx color(royalblue)(8^2) xx color(darkviolet)(13)` Plug in the known lengths `=` `3.14 xx 64 xx 9` Simplify `=` `1,808.64 \ m^3` Rounded to 2 decimal places The given measurements are in metres, so the volume is measured as metres cubedVolume`=1,808.64 \ m^3` 
Question 7 of 7
7. Question
Find the volume of the figureRound your answer to `2` decimal placesUse `pi=3.141592654` `\text(Volume )=` (1449.15, 1448.42, 1449.74) `\text(mm)^3`
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Volume of a Fractional Circle
$$\text{Volume}\;=\;\frac{\color{#e85e00}{θ}}{360°}\times π \times \color{#0079a2}{\text{radius}^2} \times \color{#9a00c7}{\text{depth}}$$Labelling the given lengths
`\text(radius)=8``theta=279°``\text(depth)=9.3`First, find the area of the front faceUse `pi=3.141592654` See `pi` explained`\text(Area)` `=` $$\frac{\color{#e85e00}{θ}}{360°}\times π \times \color{#0079a2}{\text{radius}^2}$$ Area of a Fractional Circle `=` $$\frac{\color{#e85e00}{279°}}{360°}\times π \times \color{#0079a2}{8^2}$$ Plug in the known lengths `=` $$0.775 \times 3.141592654 \times \color{#0079a2}{8^2}$$ Plug in the known lengths `=` `155.82299 \text(mm)^2` Next, multiply the area by the depth to find the volume`\text(Volume)` `=` `\text(area)``times``\text(depth)` Finding the volume `=` `155.82299``times``9.3` Plug in the known lengths `=` `1449.153807` `=` `1449.15 \text(mm)^3` Round to `2` decimal places The given measurements are in millimetres, so the volume is measured as millimetres cubed`\text(Volume)=1449.15 \text(mm)^3`The answer will depend on which `pi` you use.In this solution we used: `pi=3.141592654`.Using Answer `pi=3.141592654` `1449.15 mm^3` `pi=3.14` `1448.42 mm^3` `pi=(22)/(7)` `1449.74 mm^3`
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