SOLUTION: find the ratio of the surface areas of two cylinders whose radii are in the ratio 2:3 and have equal heights.
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-> SOLUTION: find the ratio of the surface areas of two cylinders whose radii are in the ratio 2:3 and have equal heights.
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Question 296190: find the ratio of the surface areas of two cylinders whose radii are in the ratio 2:3 and have equal heights. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! Surface area of a cylinder is equal to (2 times the area of the base) plus (the area of the height times the circumference of the cylinder).
Unfortunately, the ratio of the surface area will vary depending on the height.
I'll do an example to show you what I mean.
The surface area of the base of the cylinder is equal to .
The surface area of the cylinder itself is equal to
The total surface area is given by the equation:
S =
Assume the radius is equal to 2.
You would get:
S2 = which would become:
S2 =
Assume the radius is equal to 3.
You would get:
S3 = which would become:
S3 =
When the ratio of the radii is 2:3, your formulas become:
S2 =
S3 =
If we assume h is equal to 5, then we would get:
S2 =
S3 =
which would become:
S2 =
S3 =
which would become:
S2 =
S3 =
If we assume that h = 20, then we would get:
S2 =
S3 =
which would become:
S2 =
S3 =
which would become:
S2 =
S3 =
28/48 = .583333333
88/138 = .637681159
28/48 is not the same ratio as 88/138 so the height makes a difference.
A reference for the formula of the surface area of a cylinder is shown below:
Your problem does not appear to be worded correctly.
It needs to give the height as well, or it needs to be asking for something else, like the volume of the cylinder.
In that case, the equation for the volume of the cylinder is equal to:
V = .
You would get:
V2 = and V3 = and the ratio between V2 and V3 would be equal to 4/9.
That would remain the same regardless of the height of the cylinder and regardless of the radius of the cylinder as long as the ratio between the radii of the cylinders was the same.
This is because the and the h both cancel out in this ratio.
