Question

The difference between inside and outside surfaces of a cylindrical tube 14cm long is 88 sq. cm. If the volume of the tube is 176 cubic cm, Find the inner and outer radii of the tube.

Answer 1

Let r and R be the radii of inner and outer surfaces of a cylindrical tube,
Length of tube(h)= 14cm.
Volume of the tube =$176c{m}^3$
$\therefore \pi h(R^2-r^2)=176\Rightarrow \frac{22}{7}\times 14(R^2-r^2)=176R^2-r^2=\frac{176\times 7}{22\times 14}=4$ ....(i)
Difference of outer and inner surface of the tube = $88c{m}^3$
$2\pi h(R-r)=882\times \frac{22}{7}\times 14(R-r)=88R-r=\frac{88\times 7}{2\times 14\times 22}$ ...(ii)
But $R^2-r^2=4\Rightarrow (R+r)(R-r)=4\Rightarrow (R+r)\times 1=4\Rightarrow R+r=4$ ...(iii)
Adding (ii) and (iii),
$2R=5\Rightarrow R=\frac{5}{2}=2.5cmR+r=4\Rightarrow 2.5+r=4\Rightarrow r=4-2.5=1.5$
$\therefore$ Outer radius = 2.5cm
and inner radius = 1.5cm