Solution:

Given radius, r = 7 cm

Slant height, l = 25 cm

We know that l² = h²+r²

Height of the conical vessel, h = √(l²-r²)

= √(25²-7²)

= √(625-49)

= √576

= 24 cm

Volume of the cone = (1/3)r²h

=(1/3)×(22/7)×7²×24

= 22×7×8

= 1232 cm³

= 1.232 litres [1 litre = 1000 cm³]

Hence the volume of the cone is 1.232 litres.

(ii) Given height, h = 12 cm

Slant height, l = 13 cm

We know that l² = h²+r²

Radius of the conical vessel, r = √(l²-h²)

= √(13²-12²)

= √(169-144)

= √25

= 5 cm

Volume of the cone = (1/3)r²h

=(1/3)×(22/7)×5²×12

= (22/7)×25×4

= 2200/7 cm³

= 2.2/7 litres [1 litre = 1000 cm³]

= 0.314 litres

Hence the volume of the cone is 0.314 litres.