Question

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.

Answer 1

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.

Answer 2

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)

Answer 3

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