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.
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
To determine whether these expressions represent area or volume, we need to look at the dimensions and units involved.
1. pi(4 in)^3 / 3
In this expression, we have the cube of the radius, which indicates volume. The units are in cubic inches since it is raised to the power of 3. The "/3" part could be related to dividing by 3, which is a bit unusual for area calculations. Therefore, based on these observations, we can conclude that this expression represents volume.
2. 2pi(1.5m)^2 + 2pi(1.5m)(3m)
In this expression, we have the square of the radius and the product of the radius with another dimension. The "(1.5m)^2" part indicates area since it is squared, and the units would be in square meters. The "(1.5m)(3m)" part represents multiplying two different dimensions, which is also characteristic of an area calculation. Therefore, based on these observations, we can conclude that this expression represents area.
3. 1/2(10ft)(18ft) + (10ft)^2
In this expression, we have the product of two dimensions, "10ft" and "18ft." The "(10ft)^2" part represents the square of the dimension, which indicates area. Similarly, the "(10ft)(18ft)" part also represents the product of two dimensions, which is characteristic of an area calculation. Therefore, based on these observations, we can conclude that this expression represents area.