10.7.1 Volume Formulas

You can also use a formula to work out the volume of some of the more common solids. These are shown in the boxes below.

Volume Formulas

Volume of a rectangular box:

length multiplication width multiplication height

Volume of a cylinder:

area of base multiplication height equals pi multiplication open radius close squared postfix multiplication height

Volume of a prism:

area of base multiplication height

Volume of a sphere:

four divided by three postfix multiplication pi prefix multiplication of left parenthesis radius right parenthesis super three

Activity Symbol Activity: A Gasoline Tanker

(a) The container on a gasoline tanker is approximately cylindrical with an internal diameter of about 2.25 m and an internal length of 10 m. Roughly how many liters of gasoline could it contain?

Hint symbol

Comment

Remember that equation left hand side one m super three equals right hand side 1000 liters.

Solution Symbol

Answer

(a) If the diameter is 2.25 m, the radius = 2.25 m division two equals one .125 m. The length is 10 m.

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

volume of cylinder equation left hand side equals right hand side pi multiplication open radius close squared postfix multiplication height equation left hand side equals right hand side pi multiplication open 1.125 m close squared multiplication 10 m
equals 39.76 times m super three

Rounding to the nearest cubic meter, the volume is 40 times m super three.

Since there are 1,000 liters in one times m super three, if the tanker is full, it will hold approximately 40,000 liters.

(b) The gasoline depot 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 gasoline in the tanker?

Solution Symbol

Answer

The volume of a box equals length multiplication width multiplication height. So the volume of the underground tank equals 2.5 m multiplication four m prefix multiplication of three m equals 30 m super three. This is the same as 30,000 liters and, since this is smaller than the capacity of the tanker, not all the gasoline from the tanker would fit in the storage tank.