Question

The difference between inside and outside surface 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.

Answer 1

Length of cylindrical tube = 14 cm

Difference between the outer surface and inner surface = 88 $c{m}^2$

and volume of the tube = 176 $c{m}^3$

Let R and r be the outer and inner radius of the tube

$\therefore 2\pi Rh-2\pi rh=88$

$\Rightarrow 2\pi$ h(R-r) = 88

$\Rightarrow 2\times \frac{22}{7}\times$ 14 (R-r) = 88

$\therefore R-r=\frac{88\times 7}{2\times 22\times 14}$ = 1 cm ...(i)

and volume of the tube, $\pi R^{2}h-\pi r^2$ h = 176

$\Rightarrow \pi h(R^2-r^2)$ = 176

$\Rightarrow R^2-r^2=\frac{176\times 7}{22\times 14}$ = 4

$\Rightarrow$ (R+r) (R-r) =4 .......(ii)

Dividing (ii) by (i),

R + r = 4

and R - r = 1

Adding we get, 2R = 5$\Rightarrow R=\frac{5}{2}=2.5cm$

and subtracting, 2r = 3 $\Rightarrow r=\frac{3}{2}=1.5cm$

Hence, outer radius = 2.5 cm

and inner radius = 1.5 cm