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.
r = Inner radii of the tube
R = Outer radii of the tube
h = Length of the tube
2πh(R-r) = 88 ... (1)
πh(R2-r2) = 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}$
4-2r = 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.