VolumeUse formulae to solve problems involving the volumes of cuboids, prisms and other common solids. 
This is level 5; find the volumes of composite solid objects. You can earn a trophy if you get at least 7 questions correct and you do this activity online.
InstructionsTry your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. 



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Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.  
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© Transum Mathematics :: This activity can be found online at:
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Level 1  A basic exercise to find the number of cubes required to make the cuboid shown in the diagram
Level 2  Use the width times height times length formula to find the volume of cuboids
Level 3  Find the volumes of a wide range of prisms (including cylinders)
Level 4  Find the volumes of pyramids, cones, spheres and other common solid shapes
Level 5  Find the volumes of composite solid objects
Level 6  Find the volumes of solid objects where the units of the dimensions may differ
Surface Area  Exercises on finding the surface area of solids
Cylinders  Apply formulae for the volumes and surface areas of cylinders
Surface Area = Volume  Can you find the ten cuboids that have numerically equal volumes and surface areas? A challenge in using technology.
Exam Style Questions  A collection of problems in the style of GCSE or IB/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More on this topic including lesson Starters, visual aids, investigations and selfmarking exercises.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
See the National Curriculum page for links to related online activities and resources.
Cube: \(s^3\) where \(s\) is the length of one edge.
Cuboid: \(l\times w\times h\) where \(l\) is the length, \(w\) is the width and \(h\) is the height of the cuboid.
Cylinder: \(h \times \pi r^2\) where \(h\) is the height (or length) of the cylinder and \(r\) is the radius of the circular end.
Cone: \(h \times \frac13 \pi r^2\) where \(h\) is the height of the cone and \(r\) is the radius of the circular base.
Square based pyramid: \(h \times \frac13 s^2\) where \(h\) is the height of the pyramid and s is the length of a side of the square base.
Sphere: \(\frac43 \pi r^3\) where \(r\) is the radius of the sphere.
Prism: Area of the cross section multiplied by the length of the prism.
Unit  Relationship 

cubic metre (m^{3})  1 m^{3} = 1000 L 
litre (L)  
centilitre (cL)  100 cL = 1 L 
millilitre (mL)  1000 mL = 1 L 
cubic centimetre (cm^{3})  1000 cm^{3} = 1 L 
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Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
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Dan Walker, Twitter
Thursday, January 31, 2019