Question

The height and slant height of a conical vessel are 8 cm and 10cm respectively. Then the capacity of the vessel is _____ cu.cm.
a) 103.44
b) 401.33
c) 310.44
d) 301.71

Answer 1

Given :

A conical vessel height, (h) = 8 cm

A conical vessel slant height, (l) = 10 cm

Explanation :

As we know that formula of the volume of cone:

Volume = 1/3πr²h [cubic unit]

According to the question :

Using formula of the slant height for get radius of cone ;

Slant height,(l) = √(r)² + (h)²

➝ (l)² = (r)² + (h)²

➝ (10)² = (r)² + (8)²

➝ 100 = r² + 64

➝ r² = 100 - 64

➝ r² = 36

➝ r = √36

➝ r = 6 cm

Now,

➝ Volume of cone = 1/3πr²h

➝ Volume of cone = 1/3 × 22/7 × 6 × 6 × 8

➝ Volume of cone = 1/3 × 22/7 × 6 × 6 × 8

➝ Volume of cone = 22 × 288/21

➝ Volume of cone = 6336/21

➝ Volume of cone = 301.71 cm³

As we know that, 1cm³ = 0.001litres

➝ (301.71 × 0.001) litres

➝ 0.30171 litres .

Thus,

The capacity of conical vessel having 0.30171 litters .