A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of radius 8 cm and height 42 cm. The total space between the two vessels is filled with glass-wool for heat insulation. Find the volume of the glass-wool required.

For 1st cylindrical vessel :

Diameter (d) = 14 cm

Radius (r) = $\dfrac{\text{Diameter}}{2} = \dfrac{14}{2}$ = 7 cm

Height (h) = 42 cm

For 2nd cylindrical vessel :

Radius (R) = 8 cm

Height (H) = 42 cm

Volume of wool filled in between = Volume of 2nd cylindrical vessel - Volume of 1st cylindrical vessel

= πR²H - πr²h

= $\dfrac{22}{7} \times 8^2 \times 42 - \dfrac{22}{7} \times 7^2 \times 42$

= 22 × 64 × 6 - 22 × 49 × 6

= 8448 - 6468

= 1980 cm³.

Hence, volume of wool in between = 1980 cm³.