Transum Software

Volume

Use formulae to solve problems involving the volumes of cuboids, prisms and other common solids.

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This is level 3; find the volumes of a wide range of prisms (including cylinders). You can earn a trophy if you get at least 7 questions correct and you do this activity online.

1. Find the volume of the triangular prism. The base of the triangle is 4cm and the height of the triangle is 6cm. The length of the prism is 3cm.

Shape1
cm3 Correct Wrong

2. Find the volume of the triangular prism. The triangular end of the prism is a right-angled triangle.

Shape2
cm3 Correct Wrong

3. The cross section of this prism is in the shape of a trapezium. Find its volume.

Shape3
cm3 Correct Wrong

4. The cross section of this prism is a rhombus with an area of 24cm2. Find the volume of the prism if its length is 10cm.

Shape4
cm3 Correct Wrong

5. The cross section of this prism is a parallelogram with one pair of opposite sides 8cm long and 4cm apart. Find the volume of the prism if its length is 1.2cm.

Shape5
cm3 Correct Wrong

6. Find the volume of the large water tank given that it is a trapezoidal prism with the given dimensions.

Shape6
m3 Correct Wrong

7. Find the volume of this triangular prism

Shape7
cm3 Correct Wrong

8. Find the volume of this cylinder if its radius is 10cm and its depth is 2cm. Give your answer to three significant figures.

Shape8
cm3 Correct Wrong

9. Find the volume of this cylinder if its diameter is 3cm and its length is 11cm. Give your answer to three significant figures.

Shape9
cm3 Correct Wrong

10. Find the volume of this half cylinder which has a diameter of 12cm and a length of 8cm. Give your answer to three significant figures.

Shape10
cm3 Correct Wrong
Check

This is Volume level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 Level 6

Instructions

Try 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.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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"I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun."

Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

Whose Idea Was This?

Did you enjoy doing this 'Volume' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept.

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Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Dan Walker, Twitter

Thursday, January 31, 2019

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© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=263

Description of Levels

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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/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking 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.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Help Video

Volume Formulas

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.

Common Units

UnitRelationship
cubic metre (m3)1 m3 = 1000 L
litre (L) 
centilitre (cL)100 cL = 1 L
millilitre (mL)1000 mL = 1 L
cubic centimetre (cm3)1000 cm3 = 1 L

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Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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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