Find the capacity in litres of a conical vessel with
i) radius 7 cm, slant height 25 cm
ii) height 12 cm, slant height 13 cm .

i)Given :
Radius (r) of cone = 7 cm
Slant height (l) of cone = 25 cm

Height of cone
= \(\sqrt({l}^2 - {r}^2)\) cm
= \(\sqrt({25}^2 - {7}^2)\) cm
= \(24\) cm

We know that,

Volume of cone
= \(\frac{1}{3} {\pi} {r}^2 h\)
= \(\frac{1}{3} × \frac{22}{7} × {7}^2 × 24\) \({cm}^3\)
= 154 × 8 \({cm}^3\)
= 1232 \({cm}^3\)

Therefore, capacity of the conical vessel
= 1232 \({cm}^3\) = 1.232 litres


ii) Height (h) of cone = 12 cm
Slant height (l) of cone = 13 cm

Radius of cone
= \(\sqrt({l}^2 - {h}^2)\) cm
= \(\sqrt({13}^2 - {12}^2)\) cm
= \(5\) cm

We know that,

Volume of cone
= \(\frac{1}{3} {\pi} {r}^2 h\)
= \(\frac{1}{3} × \frac{22}{7} × {5}^2 × 12\) \({cm}^3\)
= 300 × 1.047 \({cm}^3\)
= 314.28 \({cm}^3\)

Therefore, capacity of the conical vessel = 314.28 \({cm}^3\) = 0.31428 litres