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Volume of Composite Shapes>
Volume of Composite Shapes 2Volume of Composite Shapes 2
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Question 1 of 4
1. Question
Find the volume of the figure
- `\text(Volume )=` (3420) `\text(m)^3`
Hint
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Incorrect
Volume of a Rectangular Prism
`\text(Volume )=\text(base) times \text(height) times``\text(depth)`Labelling the given lengths
`\text(Smaller Rectangle)``\text(length)=9``\text(width)=8``\text(depth)=10``\text(Larger Rectangle)``\text(length)=9``\text(width)=30``\text(depth)=10`
We need to add volume of the smaller rectangle and the larger rectangleFirst, find the area of the smaller rectangle`\text(Area)` `=` `\text(length)``times``\text(width)` `=` `9``times``8``=``72 \text(m)^2` 
Next, find the area of the larger rectangle`\text(Area)` `=` `\text(length)``times``\text(width)` `=` `9``times``30``=``270 \text(m)^2` 
Next, add the area of the smaller rectangle and the area of the larger rectangle`=` `72``+``270` Plug in the two areas `=` `342 \text(m)^2` Finally, multiply the area by the depth to find the volume`\text(Volume)` `=` `\text(area)``times``\text(depth)` Finding the volume `=` `342``times``10` Plug in the known lengths `=` `3420 \text(m)^3` The given measurements are in metres, so the volume is measured as metres cubed`\text(Volume)=3420 \text(m)^3` -
Question 2 of 4
2. Question
Find the volume of the figure
- `\text(Volume )=` (320) `\text(cm)^3`
Hint
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Incorrect
Volume of a Cube
`\text(Volume )=``\text(side)``times``\text(side)``times``\text(depth)`Labelling the given lengths
`\text(Whole Figure)``\text(side)=7``\text(depth)=8``\text(Hollow Part)``\text(side)=3``\text(depth)=8`
We need to find the volume of the figure, not including its hollow partFirst, find the area of the whole front face`\text(Area)` `=` `\text(side)^2` `=` `7^2``=``49 \text(cm)^2` 
Next, find the area of the inner shape on the front face`\text(Area)` `=` `\text(side)^2` `=` `3^2``=``9 \text(cm)^2` 
Finally, subtract the area of the inner shape from the whole shape`=` `49``-``9` Plug in the two areas `=` `40 cm^2` Next, multiply the area by the depth to find the volume`\text(Volume)` `=` `\text(area)``times``\text(depth)` Finding the volume `=` `40``times``8` Plug in the known lengths `=` `320 \text(cm)^3` The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=320 \text(cm)^3` -
Question 3 of 4
3. Question
Find the volume of the figure
Round your answer to one decimal place- `\text(Volume )=` (2120.6) `\text(m)^3`
Hint
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Incorrect
Volume of a Semicircle
`\text(Volume)=1/2 times pi times``\text(radius)^2``times``\text(height)`Labelling the given lengths
`\text(Outer Semicircle)``\text(radius)=14``\text(height)=18``\text(Inner Semicircle)``\text(radius)``=14-3=``11``\text(height)=18`
We need to find the volume of the figure, not including its hollow partNext, find the area of the Larger Semicircle`pi ~~ 3.141592654``\text(Area)` `=` `1/2 times pi times``\text(radius)^2` `=` `1/2 times pi times``14^2``=``307.88 \text(m)^2` 
Next, find the area of the Inner Semicircle`\text(Area)` `=` `1/2 times pi times``\text(radius)^2` `=` `1/2 times pi times``11^2``=``190.07 \text(m)^2` 
Now, subtract the area of the Inner Semicircle from the Outer Semicircle`=` `307.88``-``190.07` Plug in the two areas `=` `117.81 \text(m)^2` Finally, multiply the area by the height to find the volume`\text(Volume)` `=` `\text(area)``times``\text(height)` Finding the volume `=` `117.81``times``18` Plug in the known lengths `=` `2120.6 \text(m)^3` The given measurements are in metres, so the volume is measured as metres cubed`\text(Volume)=2120.6 \text(m)^3` -
Question 4 of 4
4. Question
Find the volume of air inside the Cylinder
Round your answer to two decimal places- `\text(Volume )=` (268.08) `\text(cm)^3`
Hint
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Exceptional!
Incorrect
Volume of a Cylinder
`\text(Volume)=pi times``\text(radius)^2``times``\text(height)`Volume of a Sphere
`\text(Volume)=4/3 times pi times``\text(radius)^3`Labelling the given lengths
`\text(Cylinder)``\text(radius)=?``\text(height)=16``\text(Spheres)``\text(radius)=?``\text(diameter)``=``16``divide2=``8`
We need subtract the volume of the two spheres from the volume of the cylinderFirst, recall that the radius is equal to half of the diameter`\text(radius)` `=` `1/2 times ``8` `\text(radius)` `=` `4` Since the radius is the distance from the center to any end of the circle, we can use the same value as the radius of the cylinderNext, use the formula to find the volume of the cylinder`pi ~~ 3.141592654``\text(Area)` `=` `pi times``\text(radius)^2``times``\text(height)` `=` `pi times``4^2``times``16``=``804.25 \text(cm)^3` 
Next, use the formula to find the volume of the spheres`\text(Area)` `=` `4/3 times pi times``\text(radius)^3` `=` `4/3 times pi times``4^3``=``268.08 \text(cm)^3` 
Finally, subtract the volume of the two spheres from the volume of the cylinder`=` `804.25` `-(``268.08``times 2)` Plug in the two volumes `=` `268.08 \text(cm)^3` The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=268.08 \text(cm)^3`
Quizzes
- Volume of Shapes 1
- Volume of Shapes 2
- Volume of Shapes 3
- Volume of Shapes 4
- Volume of Composite Shapes 1
- Volume of Composite Shapes 2
- Surface Area of Shapes 1
- Surface Area of Shapes 2
- Surface Area of Shapes 3
- Surface Area and Volume Mixed Review 1
- Surface Area and Volume Mixed Review 2
- Surface Area and Volume Mixed Review 3
- Surface Area and Volume Mixed Review 4