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Math - Volume Calculation











































one cubic centimeter of aluminum weighs 2.7 grams. If a piece of aluminum foil weighs 5.4 grams, find the volume of the aluminum foil.

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Sep 20, 2011
Volume Calculation Using a Ratio
by: Staff


The question:

One cubic centimeter of aluminum weighs 2.7 grams. If a piece of aluminum foil weighs 5.4 grams, find the volume of the aluminum foil.


The answer:

The easiest way to solve this problem is to use a ratio


The volume and the weight of the aluminum vary in direct proportion to each other.

Because they are directly proportional to one another, the quotient of volume divided by weight is a CONSTANT value.

Regardless of what the actual values of volume and weight, the ratio (constant) never changes.

You can set up the ratio to solve this problem as follows:

Volume of 1st aluminum sample = 1 cm³

Weight of 1st aluminum sample = 2.7 grams


Volume of 2nd aluminum sample = unknown = V₂

Weight of 2nd aluminum sample = 5.4 grams



volume of 1st aluminum sample divided by weight of 1st aluminum sample

=

volume of 2nd aluminum sample divided by the weight of 2nd aluminum sample


1 cm³ ÷ 2.7 grams

=

V₂ ÷ 5.4 grams



1 cm³ ÷ 2.7 grams = V₂ ÷ 5.4 grams

(1 cm³) /(2.7 grams) = V₂/(5.4 grams)


Now you can solve for V₂ (the volume of the 2nd aluminum sample)

I have left the units of grams and cm³ in the equation so that you can see how the units of grams cancel one another.

The units of grams and cm³ can be multiplied and divided in exactly the same way numbers can be multiplied and divided.

Only the unit cm³ will appear in the final answer because the units of grams cancel one another.


(1 cm³) / (2.7 grams) = V₂ / (5.4 grams)


To remove the 5.4 grams from the denominator on the right side of the equation, multiply each side of the equation by 5.4 grams

(5.4 grams) * [(1 cm³) / (2.7 grams)] = (5.4 grams) * [V₂ / (5.4 grams)]


Convert the 5.4 gram multiplier to a fraction on each side of the equation

(5.4 grams/1) * [(1 cm³) /(2.7 grams)] = (5.4 grams/1) * [V₂/(5.4 grams)]


rewrite the fractions on each side to show what can be cancelled.

(5.4/2.7) * (grams)/(grams) * (1 cm³)/1 = (5.4/5.4) * (grams)/(grams) * (V₂)/1


Cancel units and numbers which appear in both the numerator and denominator

(5.4/2.7) * (1) * (1 cm³)/1 = (1) * (1) * (V₂)/1


The final calculation for V₂

(5.4/2.7) * (1 cm³) = (V₂)

(2) * (1 cm³) = V₂

2 cm³ = V₂


The final answer is: V₂ = 2 cm³




Thanks for writing.

Staff
www.solving-math-problems.com



Nov 11, 2015
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by: Siavera Manga

Show me how to calculate grams to be in centimeter cubic,
Example:
5.4gram calculate into centimeter cubic













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