Cylinder Problems
1.
An 8 1/2 x 11 piece of paper can be formed into a cylinder in two different ways
- “tall” or “short.”
Without any calculations, which way, if any, has the greater volume? And
lateral area?
Put only two √ on the chart.
tall
short
same
LA
Vol
Verify your prediction by determining the lateral area and volume of each
cylinder.
tall
LA
Vol
short
same
2.
A right cylinder has a volume of 16π cubic units.
To find the minimum possible surface area, solve the equation for volume for h:
V = πr2h
Since V = 16π substitute that in the new equation and then in the equation for
surface area.
Using a graphing calculator put the surface area equation in the y=
with 0 < x < 10 and 0 < y < 200.
Find the minimum surface area.
What is the height of that cylinder?
What is that surface area?
3.
You have been asked to design a one liter oil can shaped like a right cylinder. What
dimensions will use the least amount of material?
4.
A processing plant is designing a can that can hold 64 fl oz. or 115.5 in3 and uses
the least amount of material. Find the minimum surface area.
5.
A processing plant is designing a can that can hold 60 in3 and uses the least
amount of material. Find the minimum surface area.
6.
A processing plant is designing a can that can hold 18 cu. yds. and uses the least
amount of material. Find the minimum surface area.