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 cm^{2}

Volume = 176 cm^{3}

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.