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Volume

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

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Exam-Style Description Help More...

This is level 6; find the volumes of solid objects where the units of the dimensions may differ. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

1. Calculate the number of cubic centimetres (cm3) in one cubic metre (m3).

cm3 Correct Wrong

2. Find the volume of a cube if each of its edges are of length 0.5 metres. Give your answer in cubic centimetres.

cm3 Correct Wrong

3. Use your initiative to find out how many cubic centimetres (cm3) there are in one litre.

cm3 Correct Wrong

4. A cylindrical water container has a base radius of 45cm. The container contains 36 litres of water. How deep is the water in the container? Give your answer to three significant figures.

cm Correct Wrong

5. A polythene tent is used to protect young plants from cold weather. It has a semicircular cross-section with a diameter of 80cm and a length of 7m. Find the volume of the tent in cubic metres correct to three significant figures.

m3 Correct Wrong

6. Water pours from a hosepipe (internal diameter 1.8cm) at a rate of 10 litres per minute. Calculate the speed (in centimetres per second) the water is streaming through the pipe giving your answer to the nearest whole number.

cms-1 Correct Wrong

7. Find the volume (to the nearest cubic centimetre) of a hexagonal based pyramid mounted on a plynth in the shape of a hexagonal prism of the same cross section as the base of the pyramid. If the area of the hexagon is 0.5m2 and the height of both the pyramid and the prism are 25cm.

cm3 Correct Wrong

8. A gold ingot in the shape of a cuboid (21cm x 8cm x 9cm) is melted down then cast in the shape of a cone with base radius 155mm. How tall is this cone assuming all of the gold was used? Give your answer to the nearest centimetre.

cm Correct Wrong

9. Shelly has 20 identical, spherical marbles. In order to find the radius of the marbles she immerses them in water in a cylindrical jar and notices that the water level rises by 51mm. If the jar has a base radius of 11cm find the radius of one marble in centimetres correct to the nearest millimetre.

cm Correct Wrong

10. A hollow spherical bearing has an internal radius of 60mm and an external radius of 75mm. Calculate the weight of the bearing if it is made from a metal with a density of 8.05gcm-3. Give your answer in kilograms correct to three significant figures.

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

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.

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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:

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Thursday, January 31, 2019

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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

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.

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.

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.

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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.

Log in Sign up

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