Find the capacity in litres of a conical vessel with (i) radius 7cm, slant height 25 cm (ii) height 12 cm, slant height 13 cm (Assume π = 22/7)

 Solution:

(i) Radius of cone, r =7 cm

Slant height of cone, l = 25 cm

or h = 24

Height of the cone is 24 cm

Now,

Volume of cone, V = (1/3) πr2h (formula)

V = (1/3)×(22/7) ×72×24

= (154×8)

= 1232

So, the volume of the vessel is 1232 cm3

Therefore, capacity of the conical vessel = (1232/1000) liters (because 1L = 1000 cm3)

= 1.232 Liters.

(ii) Height of cone, h = 12 cm

Slant height of cone, l = 13 cm

r = 5

Hence, the radius of cone is 5 cm.

Now, Volume of cone, V = (1/3)πr2h

V = (1/3)×(22/7)×52×12 cm3

= 2200/7

Volume of cone is 2200/7 cm3

Now, Capacity of the conical vessel= 2200/7000 litres (1L = 1000 cm3)

= 11/35 litres