Volume
What is volume?
- The volume of a 3D shape is a measure of how much space it takes up
- You need to be able to calculate the volumes of a number of common 3D shapes, including:
- Cubes and cuboids
- Prisms
- Pyramids
- Cylinders
- Spheres
How do I find the volume of a cube or a cuboid?
- A cube is a special cuboid, where the length, width and height are all of equal length
- A cuboid is another name for a rectangular-based prism
- To find the volume, V, of a cube or a cuboid, with length, l, width, w, and height, h, use the formula
- This formula is not given to you in the exam
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- You will sometimes see the terms 'depth' or 'breadth' instead of 'height' or 'width'
How do I find the volume of a prism?
- A prism is a 3D object with a constant cross-sectional area
- To find the volume, V, of a prism, with cross-sectional area, A, and length, l, use the formula
- This formula is not given to you in the exam
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- Note that the cross-section can be any shape, so as long as you know its area and the length of the prism, you can calculate its volume
- If you know the volume and length of the prism, you can calculate the area of the cross-section
- Note that the cross-section can be any shape, so as long as you know its area and the length of the prism, you can calculate its volume
How do I find the volume of a cylinder?
- To calculate the volume, V, of a cylinder with radius, r, and height, h, use the formula
- This formula is not given to you in the exam
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- Note that a cylinder is similar to a prism, its cross-section is a circle with area , and its length is h
How do I find the volume of a pyramid?
- To calculate the volume, V, of a pyramid with base area, A, and perpendicular height, h, use the formula
- This formula is given to you in the exam
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- The height must be a line from the top of the pyramid that is perpendicular to the base
- The base of a pyramid could be a square, a rectangle or a triangle
How do I find the volume of a cone?
- To calculate the volume, V, of a cone with base radius, r, and perpendicular height, h, use the formula
- This formula is given to you in the exam
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- Note that volume formula for a cone is similar to a pyramid
- The height must be a line from the top of the cone that is perpendicular to the base
How do I find the volume of a sphere?
- To calculate the volume, V, of a sphere with radius, r, use the formula
- This formula is given to you in the exam
Examiner Tip
- You only need to memorise the volume formulae for:
- Cuboids:
- Prisms:
- Cylinders:
Worked example
A cylinder is shown.
The radius, r, is 8 cm and the height, h, is 20 cm.
Calculate the volume of the cylinder, giving your answer correct to 3 significant figures.
A cylinder is similar to a prism but with a circular base
The volume of any prism, V, is its base area × height, h, where the base area here is for a circle,
Substitute r = 8 and h = 20 into the formula
Work out this value on a calculator
4021.238...
Round the answer to 3 significant figures
4020 cm3