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Volume

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

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This is level 4; find the volumes of pyramids, cones, spheres and other common solid shapes. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

1. The length of each side of the square base of the Great Pyramid of Giza is 230m. The height of the pyramid is 147m. Calculate its volume in cubic metres.

Shape1
m3 Correct Wrong

2. The base of the model pyramid shown in this diagram is a 40cm by 20cm rectangle and its height is 35cm. Calculate is volume in cubic centimetres to the nearest cubic centimetre.

Shape2
cm3 Correct Wrong

3. A tetrahedron can be thought of as a triangular-based pyramid. Calculate the volume of a tetrahedron if the area of its triangular base is 66cm2 and its height is 7cm.

Shape3
cm3 Correct Wrong

4. A right cone is a cone with its vertex above the center of its base. Calculate the volume of this right cone with a height of 4.5cm and a base radius of 3.7cm giving your answer in cubic centimetres to three significant figures.

Shape4
cm3 Correct Wrong

5. Find the volume of a sphere with a radius of 10cm giving your answer in cubic centimetres to three significant figures.

Shape5
cm3 Correct Wrong

6. A deep sea diver photographed a strange purple blob roughly in the shape of a hemisphere (half of a sphere). Calculate the volume of a hemisphere with a six centimetre diameter. Give your answer in cubic centimetres correct to three significant figures.

Shape6
cm3 Correct Wrong

7. Find the volume of a pentagonal based pyramid if the area of the pentagonal base is 33cm2, the vertical height is 6cm and one of the sloping edges is 7cm. Give your answer in cubic centimetres correct to three significant figures.

Shape7
cm3 Correct Wrong

8. Both the cylinders shown in the diagram below have the same volume. Find the width of the blue cylinder

Shape8
cm Correct Wrong

9. A solid shape has a uniform cross section of 50cm2. Its volume is 450cm2. Calculate its length in centimetres.

Shape9
cm Correct Wrong

10. The volume of a small, square-based pyramid is one thousand cubic metres. Find the length of one side of its square base if its height is eight metres. Give your answer in metres correct to three significant figures.

Shape10
m Correct Wrong
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This is Volume level 4. You can also try:
Level 1 Level 2 Level 3 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.

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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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