Functional Skills: Volume
Functional Skills: Volume Revision
Volume of 3D Shapes
The volume of an object is how much space it takes up. Volume involves lengths being multiplied 3 times – so the units for length need to be multiplied together 3 times too. Therefore, we get units like metres cubed (m^3), centimetres cubed (cm^3) and millimetres cubed (mm^3) for volume.
Make sure you are happy with the following topics before continuing.
Volume of Cubes and Cuboids
The volume of a cuboid is given by:
\text{Volume of cuboid} = \textcolor{blue}{\text{length} \times \text{width} \times \text{height} = l \times w \times h}
For a cube, all sides are the same length, so the volume of a cube is given by:
\text{Volume of cube} = \textcolor{blue}{\text{length} \times \text{length} \times \text{length} = l \times l \times l = l^3}
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Volume of Prisms and Cylinders
The volume of a prism is given by:
\text{Volume of prism} = \textcolor{red}{\text{cross-sectional area}} \times \textcolor{limegreen}{\text{length}}
This is the case for any prism, including cubes and cuboids. The cross-sectional area on a prism is the area of the front or back face. For a triangular prism, the cross-sectional area is a triangle and for a cylinder (which is like a prism) it is a circle.
So, the volume of a cylinder is given by
\text{Volume of cylinder} = \textcolor{red}{\pi r^2} \times \textcolor{limegreen}{\text{length}}
Example 1: Volume of a Cuboid
Below is a rectangle. The rectangle has a length of 18 cm, a width of 8 cm and a height of 5 cm.
Calculate the volume of the cuboid.
[2 marks]
We need to multiply the length by the width by the height.
\text{Volume} = \text{length} \times \text{width} \times \text{height} = 18 \times 8 \times 5 = 720 cm^3
Example 2: Volume of a Prism
Below is a triangular prism. The triangular face has base of 6\text{ cm} and height of 5\text{ cm}. The length of the prism is 3.5\text{ cm}.
Calculate the volume of this prism.
[3 marks]
The first step in this question is to work out the area of the cross-section, so the triangle.
We can do this as follows,
\dfrac{1}{2}(6\times5)=15\text{ cm}^2
The next step is to multiply the cross-sectional area by the length of the prism,
 \text{Volume} = 15\times3.5=52.5\text{ cm}^3
Functional Skills: Volume Example Questions
Question 1:Â The diagram below shows the outline of a cuboid, ABCDEFGH, with dimensions: AB=3 cm, BC=12 cm, and CF=16 cm.
Calculate the volume of the cuboid.
[2 marks]
Multiply the length by the height by the width:
Volume = 3\times12 \times16=576 cm^3
Question 2: Calculate the volume of a cube of sides of length 5 cm.
[2 marks]
The volume of a cube is calculated by cubing the length of one of its sides:
Volume = 5 \times 5 \times 5 = 125 cm^3
Question 3: A cylinder has a diameter of 8 cm and a length of 5 cm.
Find the volume of the cylinder, giving your answer to the nearest whole number.
Use \pi = 3.14
[3 marks]
Radius = 8 \div 2 = 4 cm
Area of circle = \pi r^2 = 3.14 \times 4^2 = 50.24 cm^2
Volume = 50.24 \times 5 = 251.2 = 251 cm^3 (nearest whole number)
Functional Skills: Volume Worksheet and Example Questions
Volume L1
FS Level 1NewOfficial PFS
Volume L2
FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]
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