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

Answer

1.5 cm, 2.5 cm

Explanation

Let the inner radius be r cm and outer radius R cm
`:. (2piRh - 2pi rh) = 88 rArr 2pi h (R -r) = 88`
`rArr 2 xx (22)/(7) xx 14 xx (R -r) = 88`
`rArr R - r = (88 xx (7)/(44 xx 14)) = 1`
`pi (R^(2) - r^(2)) xx h = 176 rArr (22)/(7) xx (R + r) xx (R -r) xx 14 = 176`
`rArr R _ r = (176)/(44) = 4 " [ :' R - r = 1]`
On solving `R + r = 4, R - r = 1`, we get
R = 2.5 cm and r = 1.5 cm