Expert: Josh - 7/25/2008

Question
i know the volume formula but i can figure out how to use that to find the radius.
the volume is 103cm3 how do i figure out the radius???

Answer
kkknorth,

The answer depends on what shape an object we are dealing with.

If it's a cylinder with radius r and height h, the volume is given by V=pi*r*r*h. If the volume V and height h are known, then, r=square_root_of(V/(pi*h)). [pi is approximately 3.1415926, you can get this from a calculator]

e.g., If V=30 cm^3, h=5 cm, then, r=sqrt(30/(pi*5))=1.3819 cm

If the object is a sphere, the volume is given by V=(4/3)*pi*r*r*r.
So, r=cubic_root((3/4)*V/pi). [cube root button on calculator looks something like ^(1/3)].

e.g., If V=30 cm^3, then, r=cubic_root((3/4)*30/pi) is approx. 1.9275 cm.
-------------------------
In case you are wondering, I have skipped a few steps of algebra. Given the volume formula V=pi*r*r*h, the idea is to rearrange the equation, making r the subject (isolate it on one side of the equation).
With V=pi*r*r*h, we divide both sides by pi, to get
V/pi=r*r*h, next we divide both sides by h, to get
V/(pi*h)=r*r, then we take the square root on both sides to get
r=sqrt(V/(pi*h)).

Similarly, with V=(4/3)*pi*r*r*r, we multiply both sides by 3/4 to get
(3/4)V=pi*r*r*r, then divide both sides by pi
(3/4)V/pi = r*r*r, finally we take the cubic root to get
r=cubic_root((3/4)*v/pi)