MTH 163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
In the following box is a question from the orientation that I do not understand the given solution for. It is taken from step 8 in the orientation, from the section on volume.
** **
Question: `q004. What is the volume of a uniform cylinder whose base has radius 5 cm and whose altitude is 30 cm?
Your solution: 2355cm^3 (A=pi*r^2, A=pi*25, A=78.5) (V=78.5*30, V=2355cm^2)
Confidence Assessment: 3
Given Solution:
`aThe cylinder is uniform, which means that its cross-sectional area is constant. So the relationship V = A * h applies.
The cross-sectional area A is the area of a circle of radius 5 cm, so we see that A = pi r^2 = pi ( 5 cm)^2 = 25 pi cm^2.
Since the altitude is 30 cm the volume is therefore
V = A * h = 25 pi cm^2 * 30 cm = 750 pi cm^3.
Note that the common formula for the volume of a uniform cylinder is V = pi r^2 h. However this is just an instance of the formula V = A * h, since the cross-sectional area A of the uniform cylinder is pi r^2. Rather than having to carry around the formula V = pi r^2 h, it's more efficient to remember V = A * h and to apply the well-known formula A = pi r^2 for the area of a circle.
** **
I understand how you got the given solution. What I don't understand is why it was left in the format 750 pi cm^3 instead of multiplying it out to the solution that I had (2355cm^3)
pi is an irrational number. 750 pi is exact. Anything else is an approximation.
Of course if you don't know the radius exactly, there's no compelling reason to give the exact result. However if you aren't sure whether the radius is to be regarded as exact, it's best to use the notation with pi.
The result 750 pi is also much easier to connect with the given information (5^2 * 30 = 750 is easy to see) than an approximate solution (difficult to see that 2355 comes from the same quantities).