(a) 1 cm.
Let the thickness of the pipe be a cm.
External Radius = 9 cm.
∴ Internal radius = (9 – a) cm.
Given, Volume of metal = 748 cm3
⇒ (π × 92 × 14) – (π × (9 – a)2 × 14) = 748
⇒ π × 14 × [81 – (81 + a2 – 18a)] = 748
⇒ –a2 + 18a = \(\frac{748}{π\times14}=\frac{748\times7}{22\times14}=17\)
⇒ a2 – 18a + 17 = 0
⇒ (a – 17) (a – 1) = 0
⇒ a = 1 or 17, but a = 17 is inadmissible.