Answer:
Note: The expression "h =300- pi r /pi r" would equate to 299, as written. I find h = (300 - π[tex]r^{2}[/tex] )/πr to be the equation for height.
Step-by-step explanation:
The total surface area of a sylinder is 2πr(h+r) where h is the height and r is the radius. That consists of top and bottom disks, each with an area of π[tex]r^{2}[/tex], for a total of 2π[tex]r^{2}[/tex]. The side is a continous sheet that has an area of 2πrh, where h is the height. 2πr is the circumference of the can, so the surface area of the side is 2πrh.
The total surace area of a closed cylinder is therefore 2π[tex]r^{2}[/tex] + 2πrh.
2π[tex]r^{2}[/tex] + 2πrh = 600
π[tex]r^{2}[/tex] + πrh = 300
πrh = 300 - π[tex]r^{2}[/tex]
h = (300 - π[tex]r^{2}[/tex] )/πr
