Succeed with maths – Part 2
Succeed with maths – Part 2

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Succeed with maths – Part 2

4.1 Volume formulas

You may have already worked out that the formula for the volume of a cuboid can be calculated using the formula shown below.

Volume of a cuboid equals length multiplication width multiplication height

Figure _unit7.4.4 Figure 29 A cuboid with the length, width and height marked

Here are the formulas of various other shapes that you may encounter as well. Remember to make a note of them somewhere, as you may need one or another for the quizzes!

Volume of cylinder

Area of base multiplication height equation left hand side equals right hand side pi multiplication radius super two postfix multiplication height

Figure _unit7.4.5 Figure 30 A cylinder with the radius of the base and the height marked

Volume of a sphere

four divided by three multiplication pi multiplication radius cubed

Figure _unit7.4.6 Figure 31 A sphere with the radius marked

Use the relevant formulas to complete this next activity and apply what you have learned in this section.

Activity _unit7.4.1 Activity 8 A fuel tanker

Timing: Allow approximately 5 minutes
  • a.The container on a fuel tanker is approximately cylindrical, with an internal diameter of about 2.25 m and an internal length of 10 m. Roughly how many cubic metres of fuel will it hold?

Answer

  • a.multiline equation line 1 Volume of a cylinder equals pi multiplication radius squared multiplication height line 2 Radius equals 2.25 m prefix division of two equals 1.125 m

    The length is 10 m, which is in this case equivalent to the height.

    Substituting these values into the formula for the volume of a cylinder:

    multiline equation line 1 Volume of a cylinder equals pi postfix multiplication left parenthesis 1.125 m right parenthesis squared multiplication 10 m line 2 equals 39.76 m super three

    Rounding to the nearest cubic metre, the volume is 40 m3.

  • b.The petrol station has an underground tank that measures 2.5 m by 4 m by 3 m. If the tank is empty, will it hold all the fuel in the tanker?

Answer

  • b.The tank must be a cuboid, as there are 3 dimensions given.

    multiline equation line 1 So the volume of the underground tank equals 2.5 m prefix multiplication of four m prefix multiplication of three m line 2 equals 30 m super three

    Since the fuel tanker will hold about 40 m3 the petrol station’s tank is not large enough to hold all the fuel.

This activity completes your study of shapes this week.

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