**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:**

*r* = Inner radii of the tube

*R* = Outer radii of the tube

*h* = Length of the tube

2π*h*(*R*-*r*) = 88 ... (1)

π*h**(**R*2-*r*2) = 176 ... (2)

Substituting *h* = 14 cm in equation (1) and (2):

π(*R-r*) = 88/28 ... (1)

π(*R-r*)(*R+r*)= 176/14 ... (2)

Simplifying the second equation by substituting it with the first equation:

$R+r=4 \mathrm{~cm}$ or $R=(4-r) \mathrm{cm}$

Re-substituting $R=4-r$ into equation (1):

$\frac{22}{7}(4-r-r)=$$\frac{88}{28}$

4-2*r* = 1

*r *= 1.5 cm

*R* = 4-1.5 = 2.5 cm

Hence, the inner and the outer radii of the tube are 1.5 and 2.5 cm, respectively.