# 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. cm3 2. Find the volume of the triangular prism. The triangular end of the prism is a right-angled triangle. cm3 3. The cross section of this prism is in the shape of a trapezium. Find its volume. cm3 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. cm3 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. cm3 6. Find the volume of the large water tank given that it is a trapezoidal prism with the given dimensions. m3 7. Find the volume of this triangular prism cm3 8. Find the volume of this cylinder if its radius is 10cm and its depth is 2cm. Give your answer to three significant figures. cm3 9. Find the volume of this cylinder if its diameter is 3cm and its length is 11cm. Give your answer to three significant figures. cm3 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. cm3
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This is Volume level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 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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