The height and slant height of a conical vessel are 12 cm and 13 cm, respectively. The capacity of the vessel is: (Use $π = 3.14$)

0.314 litres

We know that,

L² = r² + P²

volume = \(\frac{1}{3}\)πr²h

We have,

height = 12cm

slant height =13cm = L

=13² = r² + 12²

By solving further,

radius =5cm

Volume of cone =\(\frac{1}{3}\) × 3.14 × 5² × 12 = 314 = 0.314litres