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

We have,

Length of cylindrical tube = 14 cm

Let outer radius of tube = R cm

Let inner radius of tube = r cm

Difference between inside and outside surface = 88 cm²

2π (R-r) h = 88 ….. (i)

Volume of cylinder = 176 cm³

π (R² – r²) h = 176 ….. (ii)

Dividing equation (i) by equation (ii)

2π (R-r) h / π (R² – r²) h = 88/176

2 / R + r = 1/2

R+r = 4 ……. (iii)

From equation (ii)

π (R² – r²) h = 176

π (R+r) (R-r) h = 176

22/7 × 4 × (R-r) × 14 = 176

R-r = 176×7 / 22×4×14

= 1232/1232

R-r = 1 ………….. (iv)

By adding equation (iii) and (iv)

R+r = 4

R-r = 1

2R = 5

R = 5/2 = 2.5cm

R-r = 1

r = 2.5 – 1

= 1.5cm

∴ Inner and outer radii are 2.5cm and 1.5cm