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.

Answer 1

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

\[R = (4 - r)\] cm
Re-substituting

\[R = 4 - r\]into equation (1):
`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.