# Volume

## Calculate the volumes of the given solid shapes.

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

This is level 1; Find the volume of basic 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 a cube if the length of each side is 7cm. Working: cm3 Find the volume of this cuboid if:AB = 32cm, BC = 26cm and CD = 35cm. Working: cm3 Find the volume of this cylinder if the radius of the circular top is 39cm and its height is 38cm. Working: cm3 Find the volume of a cone if the radius of the circular base is 30cm and the height is 35cm. Working: cm3 Find the volume of a sphere with a diameter of 78cm. Working: cm3 Find the volume of a triangular prism if the area of its cross section is 37cm2 and its length is 44cm. Working: cm3 Find the volume of a cylinder if the diameter of the circular end is 86cm and its length is 37cm. Working: cm3 Find the volume of a square based pyramid if the length of a side of the square base is 36cm and the height is 36cm. Working: cm3 The cross section of a prism is a right angled triangle as shown in the diagram. Calculate the volume of the prism if AB = 44cm, BC = 35cm and CD = 27cm. Working: cm3 The cross section of a prism is an 'L-shaped' as shown in the diagram.     Calculate the volume of the prism if:     AB = 37cm, BC = 44cm, CD = 15cm,     DE = 8cm and AF = 10cm. Working: cm3
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## Instructions

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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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