The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq.
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

h(Rr) = 88                          … (1)      

πh(R2r2) = 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:

$R+r=4 \mathrm{~cm}$ or $R=(4-r) \mathrm{cm}$

Re-substituting $R=4-r$ into equation (1):

$\frac{22}{7}(4-r-r)=$$\frac{88}{28}$

4-2r = 1

= 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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