(I) Radius of conicon vessel r = 7 cm and slant height l = 25 cm.
Let, the height of conical vessel = h cm
We know that, l² = r² + h²
⇒ 25² = 7² + h²
⇒ 625 = 49 + h² ⇒ h² = 625 – 49 = 576
⇒ h = √576 = 24 cm
Capacity of conical vessel = 1/3πr²h
= 1/3 × 22/7 × 7 × 24 = 1232 cm³ = 1232/1000 = 1.232 litres
Hence, the capacity of conical vessel is 1.232 litres.

(II) Height of conical vessel h = 12 cm and slant height l = 13 cm
Let, the radius of conical vessel = r cm
We know that, l² = h² + r²
⇒ 13² = 12² + r²
⇒ 169 = 144 + r²
⇒ r² = 169 – 144 = 25 ⇒
r = √25 = 5 cm
Capacity of conical vessel = 1/3πr²h
= 1/3 × 22/7 × 5 × 5 × 12 = 2200/7 cm³
= 2200/(7×1000) = 11/35 litres
Hence, the capacity of conical vessel is 11/35 litres.