Volume of Shapes 1
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Question 1 of 7
1. Question
Find the volume of the Rectangular PrismThe given measurements are in units `\text(Volume )=` (48) `\text(units)^3`
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Volume of a Rectangular Prism
`\text(Volume )=``\text(side)``times``\text(side)``times``\text(depth)`In a regular cube, all sides are equalLabelling the given lengths
`\text(side)=4``\text(depth)=3`First, find the area of the front face`\text(Area)` `=` `\text(side)``times``\text(side)` Area of a Square `=` `4``times``4` Plug in the known lengths `=` `16 \text(units)^2` Next, multiply the area by the depth to find the volume`\text(Volume)` `=` `\text(area)``times``\text(depth)` Finding the volume `=` `16``times``3` Plug in the known lengths `=` `48 \text(units)^3` The given measurements are in units, so the volume is measured as units cubed`\text(Volume)=48 \text(units)^3` 
Question 2 of 7
2. Question
What is the volume of this cube?
 Volume`=` (729)`m^3`
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Volume of a Cube
`V=color(darkviolet)(s)^3`Labelling the given lengths
`color(darkviolet)(\text(side)=9)`Use the formula to find the volume`V` `=` `color(darkviolet)(s)^3` Volume of a cube formula `=` `color(darkviolet)(9)^3` Plug in the known lengths `=` `729` Simplify `=` `729 \ m^3` The given measurements are in metres, so the volume is measured as metres cubedVolume`=729 \ m^3` 
Question 3 of 7
3. Question
Find the volume of the Prism `\text(Volume )=` (696) `\text(cm)^3`
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Volume of a Triangular Prism
`\text(Volume )=1/2 times``\text(base)``times``\text(height)``times``\text(depth)`Labelling the given lengths
`\text(base)=8``\text(height)=6``\text(depth)=29`First, find the area of the front face`\text(Area)` `=` `1/2 times``\text(base)``times``\text(height)` Area of a Triangle `=` `1/2 times``8``times``6` Plug in the known lengths `=` `24 \text(cm)^2` Next, multiply the area by the depth to find the volume`\text(Volume)` `=` `\text(area)``times``\text(depth)` Finding the volume `=` `24``times``29` Plug in the known lengths `=` `696 \text(cm)^3` The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=696 \text(cm)^3` 
Question 4 of 7
4. Question
What is the volume of this Rectangular Prism?
 Volume`=` (336)`mm^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)=12)``color(darkviolet)(\text(width)=7)``color(green)(\text(depth)=4)`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(12)) xx color(darkviolet)(\text(7))xx color(green)(\text(4))` Plug in the known lengths `=` `336` `=` `336 \ mm^3` The given measurements are in millimetres, so the volume is measured as millimetres cubedVolume`=336 \ mm^3` 
Question 5 of 7
5. Question
What is the volume of this cube?
 Volume`=` (2,197)`cm^3`
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Volume of a Cube
`V=color(darkviolet)(s)^3`Labelling the given lengths
`color(darkviolet)(\text(side)=13)`Use the formula to find the volume`V` `=` `color(darkviolet)(s)^3` Volume of a cube formula `=` `color(darkviolet)(13)^3` Plug in the known lengths `=` `2,197` Simplify `=` `2,197 \ cm^3` The given measurements are in centimetres, so the volume is measured as centimetres cubedVolume`=2,197 \ cm^3` 
Question 6 of 7
6. Question
Find the volume of the CylinderRound your answer to `2` decimal placesUse `pi=3.141592654` `\text(Volume )=` (254.47, 254.34, 254.57) `\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)=3``\text(height)=9`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``3^2``times``9` Plug in the known lengths `=` `3.141592654 times 9 times 9` Simplify `=` `254.46900` `=` `254.47 \text(m)^3` Rounded to `2` decimal places The given measurements are in metres, so the volume is measured as metres cubed`\text(Volume)=254.47 \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` `254.47 m^3` `pi=3.14` `254.34 m^3` `pi=(22)/(7)` `254.57 m^3` 
Question 7 of 7
7. Question
Find the volume of the SphereRound your answer to `1` decimal placeUse `pi=3.141592654` `\text(Volume )=` (57905.8, 57876.5, 57929.1) `\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)=?``\text(diameter)=48`Recall that the radius is equal to half of the diameter`\text(radius)` `=` `1/2 times ``48` `\text(radius)` `=` `24` Now we can 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``24^3` Plug in the known lengths `=` `4/3 times 3.141592654 times 13824` Simplify `=` `57905.83579` `=` `57905.8 \text(cm)^3` Rounded to one decimal place The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=57905.8 \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` `57905.8 cm^3` `pi=3.14` `57876.5 cm^3` `pi=(22)/(7)` `57929.1 cm^3`
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