# Volume

## 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. Find the volume of this prism with dimensions:Maximum height = 17cmMinimum height = 12cmlength = 15cmWidth = 5cmTop step length = 6cm cm3 2. A three dimensional, asymetrical letter T is made up of two cuboids both 6cm wide. Calculate the volume of the shape. cm3 3. A 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 4. Use the information in the diagram of the wire frame model to calculate its volume to the nearest cubic metre. m3 5. The 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 6. An obelisc is made up of a cone on a cylinder as shown in the diagram. Calculate its volume to the nearest cubic metre. m3 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 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 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 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
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This is Volume level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6

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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

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).

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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.

## 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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