Volume of Shapes 2
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Question 1 of 8
1. Question
Find the volume of the Parallelogram `\text(Volume )=` (280) `\text(cm)^3`
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Volume of a Parallelogram
`\text(Volume )=``\text(base)``times``\text(height)``times``\text(depth)`Labelling the given lengths
`\text(base)=7``\text(height)=5``\text(depth)=8`First, find the area of the front face`\text(Area)` `=` `\text(base)``times``\text(height)` Area of a Paralellogram `=` `7``times``5` Plug in the known lengths `=` `35 \text(cm)^2` Next, multiply the area by the depth to find the volume`\text(Volume)` `=` `\text(area)``times``\text(depth)` Finding the volume `=` `35``times``8` Plug in the known lengths `=` `280 \text(cm)^3` The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=280 \text(cm)^3` 
Question 2 of 8
2. Question
What is the volume of this cube?
 Volume`=` (343)`mm^3`
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Volume of a Cube
`V=color(darkviolet)(s)^3`Labelling the given lengths
`color(darkviolet)(\text(side)=7)`Use the formula to find the volume`V` `=` `color(darkviolet)(s)^3` Volume of a cube formula `=` `color(darkviolet)(7)^3` Plug in the known lengths `=` `343` Simplify `=` `343 \ mm^3` The given measurements are in millimetres, so the volume is measured as millimetres cubedVolume`=343 \ mm^3` 
Question 3 of 8
3. Question
What is the volume of this Rectangular Prism?
 Volume`=` (40)`m^3`
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Volume of a Rectangular Prism
`V=color(royalblue)(\text(height)) xx color(darkviolet)(\text(width))xx color(green)(\text(depth))`Labelling the given lengths
`color(royalblue)(\text(height)=2)``color(darkviolet)(\text(width)=10)``color(green)(\text(depth)=2)`Use the formula to find the volume`V` `=` `color(royalblue)(\text(height)) xx color(darkviolet)(\text(width))xx color(green)(\text(depth))` Volume of a Rectangular Prism formula `=` `color(royalblue)(\text(2)) xx color(darkviolet)(\text(10))xx color(green)(\text(2))` Plug in the known lengths `=` `40` `=` `40 \ m^3` The given measurements are in metres, so the volume is measured as metres cubedVolume`=40 \ m^3` 
Question 4 of 8
4. Question
Find the volume of the Prism `\text(Volume )=` (1092) `\text(m)^3`
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Volume of a Trapezoidal Prism
`\text(Volume )=1/2 times``\text(height)``times (``\text(base)_1``+``\text(base)_2``)``times``\text(depth)`Labelling the given lengths
`\text(height)=12``\text(base)_1=8``\text(base)_2=18``\text(depth)=7`First, find the area of the front face`\text(Area)` `=` `1/2 times``\text(height)``times (``\text(base)_1``+``\text(base)_2``)` Area of a Trapezoid `=` `1/2 times``12``times (``8``+``18``)` Plug in the known lengths `=` `156 \text(m)^2` Next, multiply the area by the depth to find the volume`\text(Volume)` `=` `\text(area)``times``\text(depth)` Finding the volume `=` `156``times``7` Plug in the known lengths `=` `1092 \text(m)^3` The given measurements are in metres, so the volume is measured as metres cubed`\text(Volume)=1092 \text(m)^3` 
Question 5 of 8
5. Question
What is the volume of this Triangular Prism?
 Volume`=` (2002)`m^3`
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Volume of a Triangular Prism
`V=1/2 xx color(darkviolet)(\text(base)) xx color(royalblue)(\text(height)) xx color(green)(\text(depth))`Labelling the given lengths
`color(darkviolet)(\text(base)=14)``color(royalblue)(\text(height)=13)``color(green)(\text(depth)=22)`Use the formula to find the volume`V` `=` `1/2 xx color(darkviolet)(\text(base)) xx color(royalblue)(\text(height)) xx color(green)(\text(depth))` Volume of a Triangular Prism formula `=` `1/2 xx color(darkviolet)(\text(14))xx color(royalblue)(\text(13)) xx color(green)(\text(22))` Plug in the known lengths `=` `2,002` `=` `2,002 \ m^3` The given measurements are in metres, so the volume is measured as metres cubedVolume`=2,002 \ m^3` 
Question 6 of 8
6. Question
Find the volume of the CylinderRound your answer to `1` decimal placeUse `pi=3.141592654` `\text(Volume )=` (415122.2, 414911.8, 415289.3) `\text(m)^3`
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Volume of a Cylinder
`\text(Volume)=pi times``\text(radius)^2``times``\text(height)`Labelling the given lengths
`\text(radius)=?``\text(diameter)=155``\text(height)=22`Recall that the radius is equal to half of the diameter`\text(radius)` `=` `1/2 times ``155` `\text(radius)` `=` `77.5` Now we can use the formula to find the volumeUse `pi=3.141592654` See `pi` explained`\text(Volume)` `=` `pi times``\text(radius)^2``times``\text(height)` Volume of a Cylinder formula `=` `3.141592654 times``77.5^2``times``22` Plug in the known lengths `=` `3.141592654 times 6006.25 times 22` Simplify `=` `415122.1993` `=` `415122.2 \text(m)^3` Rounded to one decimal place The given measurements are in metres, so the volume is measured as metres cubed`\text(Volume)=415122.2 \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` `415122.2 m^3` `pi=3.14` `414911.8 m^3` `pi=(22)/(7)` `415289.3 m^3` 
Question 7 of 8
7. Question
Find the volume of the SphereRound your answer to the nearest whole numberUse `pi=3.141592654` `\text(Volume )=` (17157, 17149, 17164) `\text(cm)^3`
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Volume of a Sphere
`\text(Volume)=4/3 times pi times``\text(radius)^3`Labelling the given lengths
`\text(radius)=16`Use the formula to find the volumeUse `pi=3.141592654` See `pi` explained`\text(Volume)` `=` `4/3 times pi times``\text(radius)^3` Volume of a Sphere formula `=` `4/3 times 3.141592654 times``16^3` Plug in the known lengths `=` `4/3 times 3.141592654 times 4096` Simplify `=` `17157.28468` `=` `17157 \text(cm)^3` Rounded to a whole number The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=17157 \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` `17157 cm^3` `pi=3.14` `17149 cm^3` `pi=(22)/(7)` `17164 cm^3` 
Question 8 of 8
8. Question
Find the volume of the HemisphereRound your answer to `1` decimal placeUse `pi=3.141592654` `\text(Volume )=` (9408.3, 9403.5, 9412.1) `\text(cm)^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)=?``\text(diameter)=33`Recall that the radius is equal to half of the diameter`\text(radius)` `=` `1/2 times ``33` `\text(radius)` `=` `16.5` Now we can 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``16.5^3` Plug in the known lengths `=` `1/2 times 4/3 times 3.141592654 times 4492.125` Simplify `=` `9408.28459` `=` `9408.3 \text(cm)^3` Rounded to one decimal place The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=9408.3 \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` `9408.3 cm^3` `pi=3.14` `9403.5 cm^3` `pi=(22)/(7)` `9412.1 cm^3`
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