# Volume

## Calculate the volumes of the given solid shapes.

##### Level 1Level 2Level 3FormulasSurface AreaDescriptionMore 3D

This is level 2; Find the volume of compound solid shapes. Give non-exact answers correct to the nearest whole number of the indicated units. The diagrams are not to scale.

 Find the volume of this prism with dimensions:Maximum height = 17cmMinimum height = 12cmlength = 15cmWidth = 5cmTop step length = 6cm Working: cm3 A three dimensional, asymetrical letter T is made up of two cuboids both 6cm wide. Calculate the volume of the shape. Working: cm3 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 to the nearest cubic metre. Working: cm3 Use the information in the diagram of the wire frame model to calculate its volume to the nearest cubic metre. Working: cm3 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. Working: cm3 An obelisc is made up of a cone on a cylinder as shown in the diagram. Calculate its volume to the nearest cubic metre. Working: cm3 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. Working: cm3 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? Working: cm3 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. Working: cm3 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. Working: cm3
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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:

David Whitaker, Princes Risborough

Wednesday, May 4, 2016

"I have been trying to work out the solutions to the level 1 questions on the volumes of cylinders, cones and spheres, but have been unsuccessful despite entering various values for pi. Can you advise what value I should use.
Thank You

[Transum: Typically the value of pi stored on your calculator (roughly 3.141592) should be used for those questions and did you notice the instruction at the top of the page that stated 'Give non-exact answers correct to the nearest whole number of the indicated units'?]"

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## Description of Levels

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Level 1 - Find the volume of basic solid shapes.

Level 2 - Find the volume of compound solid shapes.

Level 3 - Exam-type questions on mensuration.

You could also try the Surface Area exercise.

## 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.

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