Applications of Volume

We've already learnt about volume and how to find the volume of different types of solids, including prisms, cylinders, composite solids, pyramids, cones and spheres.  

Now let's look at how we can apply these formulae to different situations in the real world.

 

Examples

Question 1

Question 2

The formula relating density ($D$D), mass ($M$M) and volume ($V$V) is $D=\frac{M}{V}$D=MV​.

A file has a density of $7.2$7.2 grams per cubic centimetre. It also has a mass of $100.8$100.8 grams. What is the file’s volume, $V$V?

Think: We need to substitute the values in that we know to find the one we don't know.

Do:

$D$D	$=$=	$\frac{M}{V}$MV​
$7.2$7.2	$=$=	$\frac{100.8}{V}$100.8V​
$7.2V$7.2V	$=$=	$100.8$100.8
$V$V	$=$=	$\frac{100.8}{7.2}$100.87.2​
	$=$=	$14$14 $cm^3$cm3

 

Question 3

Which cordial is stronger (has a higher concentration)?

A) $3L$3L of cordial made with $100mL$100mL of concentrate

B) $2L$2L of cordial made with $1L$1L of concentrate

Think: Cordial is made up of concentrate and water. The stronger cordial will be the one with less water. We need to make the amount of concentrate or the total amount of cordial equivalent in the two options so we can make a meaningful comparison.

Do: I am going to change (A) so it is in terms of $1L$1L of concentrate. To do this, I need to multiply both sides by $10$10 because $1000mL=1L$1000mL=1L.

$3L/100mL$3L/100mL

$=$=

$30L/L$30L/L

This means that $1L$1L of concentrate is used to make $30L$30L of cordial in (A) and only $2L$2L of cordial in B.

So B) $2L$2L of cordial made with $1L$1L of concentrate is the stronger rate.

Question 4

Question 5