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 radius of the tube.

Answer 1

Given,

length of cylindrical tube = 14 cm

Difference between inside and outside surface = 88 cm²

volume of cylinder = 176 cm³

let outer radius of tube = R cm

Let inner radius of tube = r cm

so,

= 2π(R - r)h = 88 ... ... ... ... (i)

= π(R² - r²)h = 176 .. ... .. . ...(ii)

dividing equation (i) by equation (ii)

= \(\frac{[2π(R-r)h]}{[π(R+r)(R-r)]}\) = \(\frac{88}{176}\) = \(\frac{1}{2}\)

= \(\frac{2}{R+r}\) = \(\frac{1}{2}\)

= R + r = 4 ..................(iii)

from equation (ii)

= π(R + r)(R - r)h = 176

= \(\frac{22}{7}\)x 4 x (R - r) x 14 = 176

= R - r = 1 ... . . .. . (iv)

from equation (iii) and (iv)

= 2R = 5

= R = \(\frac{5}{2}\) = 2.5 cm

= r = 1.5 cm