Find the capacity in liters of a conical vessel with 

(i) radius 7 cm, slant height 25 cm 

(ii) height 12 cm, slant height 13 cm

We know that, Capacity of the conical vessel = 1/3 πr²h

(i) Radius, r = 7cm

Slant height, l = 25cm

We know that l² = h² +r²

h² = (25)² - (7)²

= 625 - 49 = 576

h = 24 cm

Using the above formula, we have 

V = = (1/3)×(22/7) ×7²×24

= 154×8 = 1232 

So, the volume of the vessel is 1232 cm³

Therefore, the capacity of the conical vessel = 1232/1000 = 1.232 Liters.

(ii) Height, h = 12 cm

Slant height, l = 13 cm

We know that l² = h² +r²

r² = (13)² - (12)²

= 169 - 144 = 25

r = 5 cm

Using the above formula, we have 

V = (1/3) × (22/7) × 52 × 12

= 2200/7

The volume of the cone is 2200/7 cm³

Now, Capacity of the conical vessel= 2200/7000 = 11/35 litres