A cylinder has a radius of 4 cm and volume of 800 cm3. A similar cylinder with the same height has a volume of 200 cm3. Find the radius of the smaller cylinder.

Firstly, we have to understand how the radius of the first cylinder was used to calculate its volume. Then we can use that understanding to then use the information we have about the other cylinder to calculate its radius.A cylinder is defined by the circle and its height. So in order to calculate the volume we need to use the radius to calculate the area of the circle. (area = piarea squared)From there we need to add the height of the cylinder to get its volume. This changes the formula to:volume = piarea squaredheightPlugging in what we now about the cylinder gets us 800cm3 = pi(4cm4cm)heightRearranging that gets us800cm3/16cm2 = pihWhich can be solved for hh = 800cm3/(16cm2pi) = 50cm/piFor the second cylinder we are going to start with the same formula and keep the height we got from the first cylinder in mind.volume = piradius squaredheightWe are going to rearrange that to have r on one side and everything else on the other sideradius = square root of (volume/(piheight))And now we are going to plug in everything we know (namely, V and h)radius = square root of (200cm3/(pi(50cm/pi))) = square root of (200cm3/50cm) = square root of (4cm2) = 2cm