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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
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: \[R + r = 4\] cm or
Re-substituting
`22/7`(4-r-r) = `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.
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