I have determine if these are area or volume simply based on looking at them without doing the calculations. Could you please explain how to do that?

1. pi(4 in)^3 is in the numerator
3 is in the denominator

2. 2pi(1.5m)^2 + 2pi(1.5m)(3m)

3. 1/2(10ft)(18ft) + (10ft)^2

Thank you.

3 answers

If the length unit is, say, ft, then

length is in ft
area is in ft^2
volume is in ft^3

So, see what the power of the unit is to determine the quantity being measured.
Steve,

Thank you. How does it work, then, when you have both squared and cubed such as:

2(4/3(1.5m)^3) + pi(1.5m)^2(3m)
your example is simply volume. Look at the units. You have

m^3 + m^2 * m
but
m^2 * m = m^3

so both terms are volume