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Question
The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq. cm. If the volume of the tube is 176 cubic cm, find the inner and outer radii of the tube.
Solution
Given data is as follows:
h = 14 cm
Outer Curved Surface Area − Inner Curved Surface Area = 88 cm2
Volume = 176 cm3
We have to find the inner and outer radii of the tube.
As given in the problem we have,
` 2piRh - 2 pirh = 88`
`2xx22/7xx14(R-r)=88`
`R - r = 1`
Also, from the given data we have,
`piR^2h - pir^2h = 176`
`pih(R^2 - r^2) = 176`
`22/7 xx 14 xx (R-r)(R + r) = 176`
`(R - r)(R + r) = 4`
We have already found out that R - r = 1
Therefore,
R + r = 4
Now let us solve these two equations, by adding them
R - r = 1
R + r = 4
We get
2R = 5
R = 2.5
Substituting for R in R -r =1 , we get
r = 1.5
Thus, inner radius of the pipe is equal to 1.5 cm and outer radius of the pipe is equal to 2.5 cm.
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