SOLUTION: A 5 inch by 8 inch rectangular piece of paper can be rolled up to form either of two right circular cylinders, a cylinder with a height of 8 inches or a cylinder with a height of 5

Question 1044591: A 5 inch by 8 inch rectangular piece of paper can be rolled up to form either of two right circular cylinders, a cylinder with a height of 8 inches or a cylinder with a height of 5 inches. What is the ratio of the volume of the 8 inch tall cylinder to the volume of the 5 inch tall cylinder?
Found 2 solutions by Cromlix, ikleyn:
Answer by Cromlix(4381)   (Show Source): You can put this solution on YOUR website!
Hi there,,
Considering cylinder of 8" height.
It will have a circumference of 5"
To find radius:
Circumference = 2πradius
2πradius = 5"
πradius = 2.5"
Radius = 2.5"/π
Volume = πr^2h
Volume = π(2.5/π)^2 x 8
Volume = 15.91 ins^3
........................
Considering cylinder of 5" height.
It will have a circumference of 8"
To find radius:
Circumference = 2πradius
2πradius = 8"
πradius = 4"
Radius = 4"/π
Volume = πr^2h
Volume = π(4/π)^2 x 5
Volume = 25.46 ins^3
.................
Ratio of volume of 8" tall cylinder
to volume of 5" tall cylinder
15.91 ins^3 to 25.46 ins^3
1 : 1.6.
Hope this helps :-)
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
On surface area and volume of cylinders see the lesson
    - Surface area of cylinders
in this site.

On volumes of cylinders see the lesson
    - Volume of cylinders
in this site.

For surface area and volumes of other solid bodies see the associate lessons.

You have also free of charge online textbook on Geometry in this site
    GEOMETRY - YOUR ONLINE TEXTBOOK

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