# 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. - Mathematics

Sum

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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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Exercise 19.2 | Q 28 | Page 22