How do you calculate the volume of an object?
Worked examples: Volume
The volume of a solid is the amount of material the solid contains. Units are written as mm 3
(cubic millimetres), m3 (cubic metres), in3 (cubic inches), or ft3 (cubic feet).
You can calculate the volume of some regular shapes if you know the right formula.
What is the volume of this cube?
The formula for the volume of a cube is V = S³
Substitute the actual dimensions
V = 600 x 600 x 600
V = 216000000mm3 (Note that the answer for volume problems is given in cubic units.)
You could also do the same problem, using the same formula, in units of metres.
600mm = 0.6 metres
Substitute the actual dimension
V = 0.6 x 0.6 x 0.6 = 0.216m3
What is the volume of this rectangular solid?
The formula for the volume of a rectangular solid is V = L x b x d
Substitute the actual dimensions
V = 550 x 450 x 200
V = 49500000mm3 (Note that the answer for volume problems is given in cubic units.)
Activity sheet: How do you calculate the volume of an object
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What is the volume of this triangular prism?
This is a right angled prism, that is, one of the sides has the same length as the vertical height
to the apex.
The formula for the volume of a triangular prism is V = l x bh
2
Substitute the actual dimensions
V = 300 x 100 x 450
2
V = 6750000mm3 (Note that the answer for volume problems is given in cubic units.)
What is the volume of this disk?
The formula for calculating the volume of a disk is
V=  D² x t
4
Substitute the actual dimensions
V =  x 450 x 450 x 100
4
V = 15904312.8088mm3 (Note that the answer for volume problems is given in cubic units.)
V = 15904313mm3
Activity sheet: How do you calculate the volume of an object
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Volume problems
1. What is the volume of a rectangular solid with sides 425mm, 100mm and 330mm?
2. You have to fill 8 cubical tanks. Each tank has internal dimensions of 260mm by 260mm by 260mm.
What is the total volume you have to fill?
3. A triangular prism stands on a base that is 135mm long. The apex, or top of the triangle, is 200mm above
the base and the prism is 100mm thick. What volume is contained in the prism?
4. A small metal disk has a top 120mm in diameter. If the disk is 16mm thick, what volume does it contain?
5. You have nine disk shaped fuel tanks. Each has a diameter of 825mm and is 125mm high. What is the
total volume of fuel required to fill all the tanks?
Check your responses with the answers below.
Answers
(1) 14025000mm3
(2) 17576000mm3
(4) 180956mm3
(5) 66820203mm3
(3) 2700000mm3
Activity sheet: How do you calculate the volume of an object
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