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Find the capacity in litres of a conical vessel withi) 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

= $$\sqrt({l}^2 - {h}^2)$$ 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