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

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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.

1. Composite 3DShapeFind the volume of this prism with dimensions:
Maximum height = 17cm
Minimum height = 12cm
length = 15cm
Width = 5cm
Top step length = 6cm

cm3 Correct Wrong

2. Composite 3DShapeA three dimensional, asymetrical letter T is made up of two cuboids both 6cm wide. Calculate the volume of the shape.

cm3 Correct Wrong

3. Composite 3DShapeA beach hut is in the shape of a triangular prism on a cuboid. Find the volume of the hut from the measurements given on the diagram. Give your answer to the nearest cubic metre.

m3 Correct Wrong

4. Composite 3DShapeUse the information in the diagram of the wire frame model to calculate its volume to the nearest cubic metre.

m3 Correct Wrong

5. Composite 3DShapeThe model of a building to house a telescope is in the shape of a hemisphere on a cylinder. Calculate the volume of the model to the nearest cubic centimetre.

cm3 Correct Wrong

6. Composite 3DShapeAn obelisc is made up of a cone on a cylinder as shown in the diagram. Calculate its volume to the nearest cubic metre.

m3 Correct Wrong

7. A hollow brass cone has an outer radius of 60cm and an inner radius of 50cm. The outer height is 90cm and the inner height is 70cm. Find the volume of brass in the cone to the nearest cubic centimetre.

cm3 Correct Wrong

8. Twenty ball bearings each with a radius of 5cm are melted down and cast into a cuboid of lenght 20cm and width 40cm. What is the height of this cuboid to the nearest centimetre?

cm Correct Wrong

9. A hemisphere and a cone are joined at their identical 8.8cm radius circular bases. The length of the composite solid as measured from the apex of the cone is 19.5cm. Find the volume of the solid in cubic centimetres to the nearest cubic centimetre.

cm3 Correct Wrong

10. A circular hole of diameter 7mm is drilled through a cuboid of dimensions 10mm by 12 mm by 14mm. The hole starts at the centre of one of the faces of the cuboid and goes through to the centre of the opposite face. What is the maximum possible volume of wood remaining after the hole has been drilled? Give your answer in cubic millimetres to three significant figures.

mm3 Correct Wrong

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


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

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Thursday, January 31, 2019

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Description of Levels



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

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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