Topics
>
Geometry>
Surface Area and Volume>
Volume of Composite Shapes>
Volume of Composite Shapes 1Volume of Composite Shapes 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- Answered
- Review
-
Question 1 of 5
1. Question
Find the volume of the figure
- `\text(Volume )=` (25200) `\text(cm)^3`
Hint
Help VideoCorrect
Correct!
Incorrect
Volume of a Rectangular Prism
`\text(Volume )=\text(length) times \text(width) times``\text(depth)`Labelling the given lengths
`\text(Smaller Rectangle)``\text(length)=30``\text(width)=20``\text(depth)=12``\text(Larger Rectangle)``\text(length)=60``\text(width)=25` `(55-``30``)``\text(depth)=12`
First, find the area of the smaller rectangle`\text(Area)` `=` `\text(length)``times``\text(width)` `=` `30``times``20``=``600 \text(cm)^2` 
Next, find the area of the larger rectangle`\text(Area)` `=` `\text(length)``times``\text(width)` `=` `60``times``25``=``1500 \text(cm)^2` 
Next, add the area of the smaller rectangle and the area of the larger rectangle`=` `600``+``1500` Plug in the two areas `=` `2100 \text(cm)^2` Finally, multiply the area by the depth to find the volume`\text(Volume)` `=` `\text(area)``times``\text(depth)` Finding the volume `=` `2100``times``12` Plug in the known lengths `=` `25200 \text(cm)^3` The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=25200 \text(cm)^3` -
Question 2 of 5
2. Question
Find the volume of the figure
Round your answer to the nearest whole numberUse `pi=3.141592654`- `\text(Volume )=` (31616, 31605, 31625) `\text(cm)^3`
Hint
Help VideoCorrect
Nice Job!
Incorrect
Volume of a Rectangular Prism
`\text(Volume )=``\text(length)``times``\text(breadth)``times``\text(height)`Volume of a Cone
`\text(Volume)=1/3 times pi times``\text(radius)^2``times``\text(height)`Labelling the given lengths
`\text(Cone)``\text(radius)=18``\text(height)=62``\text(Rectangular Prism)``\text(length)=46``\text(breadth)=46``\text(height)=5`
First, find the area of the rectangle`\text(Area)` `=` `\text(length)``times``\text(breadth)` `=` `46``times``46``=``2116 \text(cm)^2` 
Next, multiply the area by the height to find the volume`\text(Volume)` `=` `\text(area)``times``\text(height)` Finding the volume `=` `2116``times``5` Plug in the known lengths `=` `10580 \text(cm)^3` Next, use the formula to find the volume of the coneUse `pi=3.141592654` See `pi` explained`\text(Volume)` `=` `1/3 times pi times``\text(radius)^2``times``\text(height)` `=` `1/3 times 3.141592654 times``18^2``times``62` `=` `21036.10441 \text(cm)^3` 
Finally, add the volume of the cube and the volume of the cone`=` `10580``+``21036.10441` Plug in the two volumes `=` `31616.10441` `=` `31616 \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)=31616 \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` `31616 cm^3` `pi=3.14` `31605 cm^3` `pi=(22)/(7)` `31625 cm^3` -
Question 3 of 5
3. Question
Find the volume of the figure
Round your answer to `2` decimal placesUse `pi=3.141592654`- `\text(Volume )=` (179.07, 178.98, 179.14) `\text(cm)^3`
Hint
Help VideoCorrect
Well Done!
Incorrect
Volume of a Hemisphere
`\text(Volume)=1/2 times 4/3 times pi times``\text(radius)^3`Volume of a Cone
`\text(Volume)=1/3 times pi times``\text(radius)^2``times``\text(height)`Labelling the given lengths
`\text(radius)=?``\text(diameter)=6``\text(height)=13`
We need to add volume of the hemisphere and the coneFirst, recall that the radius is equal to half of the diameter`\text(radius)` `=` `1/2 times ``6` `\text(radius)` `=` `3` Next, use the formula to find the volume of the hemisphereUse `pi=3.141592654` See `pi` explained`\text(Volume)` `=` `1/2 times 4/3 times pi times``\text(radius)^3` `=` `1/2 times 4/3 times 3.141592654 times``3^3` `=` `56.54866 \text(cm)^3` 
Next, use the formula to find the volume of the coneUse `pi=3.141592654` See `pi` explained`\text(Volume)` `=` `1/3 times pi times``\text(radius)^2``times``\text(height)` `=` `1/3 times 3.141592654 times``3^2``times``13` `=` `122.52211 \text(cm)^3` 
Finally, add the volume of the sphere and the volume of the cone`=` `56.54866``+``122.52211` Plug in the two volumes `=` `179.07078` `=` `179.07 \text(cm)^3` Rounded to `2` decimal places The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=179.07 \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` `179.07 cm^3` `pi=3.14` `178.98 cm^3` `pi=(22)/(7)` `179.14 cm^3` -
Question 4 of 5
4. Question
Find the volume of the figure
Note: The cylinder is hollowRound your answer to `2` decimal placesUse `pi=3.141592654`- `\text(Volume )=` (2211.68, 2210.56, 2212.57) `\text(cm)^3`
Hint
Help VideoCorrect
Keep Going!
Incorrect
Volume of a Cylinder
`\text(Volume)=pi times``\text(radius)^2``times``\text(height)`Labelling the given lengths
`\text(Outer Cylinder)``\text(radius)=?``\text(diameter)=12``\text(height)=22``\text(Inner Cylinder)``\text(radius)=2``\text(height)=22`
We need to find the volume of the figure, not including its hollow partFirst, recall that the radius is equal to half of the diameter`\text(radius)` `=` `1/2 times ``12` `\text(radius(Larger Circle))` `=` `6` Next, use the formula to find the area of the Outer CircleUse `pi=3.141592654` See `pi` explained`\text(Area)` `=` `pi times``\text(radius)^2` `=` `3.141592654 times``6^2` `=` `113.09733 \text(cm)^2` 
Next, find the area of the Inner CircleUse `pi=3.141592654` See `pi` explained`\text(Area)` `=` `pi times``\text(radius)^2` `=` `3.141592654 times``2^2` `=` `12.56637 \text(cm)^2` 
Now, subtract the area of the Inner Circle from the Outer Circle`=` `113.09733``-``12.56637` Plug in the two areas `=` `100.53096 \text(cm)^2` Finally, multiply the area by the height to find the volume`\text(Volume)` `=` `\text(area)``times``\text(height)` Finding the volume `=` `100.53096``times``22` Plug in the known lengths `=` `2211.68122` `=` `2211.68 \text(cm)^3` Rounded to `2` decimal places The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=2211.68 \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` `2211.68 cm^3` `pi=3.14` `2210.56 cm^3` `pi=(22)/(7)` `2212.57 cm^3` -
Question 5 of 5
5. Question
Find the volume of the figure
Round your answer to two decimal places- `\text(Volume )=` (508.94, 508.68, 509.14) `\text(cm)^3`
Correct
Well Done!
Incorrect
Volume of a Cylinder
`\text(Volume)=pi times``\text(radius)^2``times``\text(height)`Labelling the given lengths
`\text(Short Cylinders)``\text(radius)=?``\text(diameter)=12``\text(height)=2``\text(Long Cylinder)``\text(radius)=?``\text(diameter)=3``\text(height)=8`
First, recall that the radius is equal to half of the diameter`\text(radius)` `=` `1/2 times ``12` `\text(radius(short cylinders))` `=` `6` ` ` ` ` ` ` `\text(radius)` `=` `1/2 times ``3` `\text(radius(long cylinder))` `=` `1.5` Next, use the formula to find the volume of the two short cylindersUse `pi=3.141592654` See `pi` explained`\text(Volume)` `=` `3.141592654 times``\text(radius)^2``times``\text(height)` `=` `3.141592654 times``6^2``times``2` `=` `226.19467` Since there are two short cylinders, we multiply our answer by two.`\text(Volume)` `=` `226.19467 times 2` `=` `452.38934 \text(cm)^3` 
Now, use the formula to find the volume of the long cylinderUse `pi=3.141592654` See `pi` explained`\text(Volume)` `=` `3.141592654 times``\text(radius)^2``times``\text(height)` `=` `3.141592654 times``1.5^2``times``8` `=` `56.54866 \text(cm)^3` 
Finally, add the volume of the two short cylinders and the volume of the long cylinder`=` `452.38934``+``56.54866` Plug in the two volumes `=` `508.938` `=` `508.94 \text(cm)^3` Rounded to `2` decimal places The given measurements are in centimetres, so the volume is measured as centimetres cubed`\text(Volume)=508.94 \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` `508.94 cm^3` `pi=3.14` `508.68 cm^3` `pi=(22)/(7)` `509.14 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