Find the capacity in litres of a conical vess | vedclass

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(C) Given: Height $(h) = 12 \,cm$ and slant height $(l) = 13 \,cm$.First,we find the radius $(r)$ using the relation $l^2 = r^2 + h^2$.$r = \sqrt{l^2

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$\frac{11}{35} \,l$

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(C) Given: Height $(h) = 12 \,cm$ and slant height $(l) = 13 \,cm$.First,we find the radius $(r)$ using the relation $l^2 = r^2 + h^2$.$r = \sqrt{l^2 - h^2} = \sqrt{13^2 - 12^2} = \sqrt{169 - 144} = \sqrt{25} = 5 \,cm$.Now,the volume $(V)$ of the conical vessel is given by the formula $V = \frac{1}{3} \pi r^2 h$.$V = \frac{1}{3} 	imes \frac{22}{7} 	imes (5)^2 	imes 12 \,cm^3$.$V = \frac{1}{3} 	imes \frac{22}{7} 	imes 25 	imes 12 = 22 	imes 25 	imes \frac{4}{7} = \frac{2200}{7} \,cm^3$.Since $1000 \,cm^3 = 1 \,l$,the capacity in litres is $\frac{2200}{7 	imes 1000} \,l = \frac{22}{70} \,l = \frac{11}{35} \,l$.Thus,the capacity of the conical vessel is $\frac{11}{35} \,l$.

Find the capacity in litres of a conical vessel with height $12 \,cm$ and slant height $13 \,cm$.

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