The radius and slant height of a conical vess | vedclass

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Question

(A) Given: Radius $(r)$ = $35 \,cm$,Slant height $(l)$ = $91 \,cm$.First,find the vertical height $(h)$ using the relation $l^2 = r^2 + h^2$.$h = \sqr

Vedclass · Accepted Answer

$107$

Vedclass · Answer

(A) Given: Radius $(r)$ = $35 \,cm$,Slant height $(l)$ = $91 \,cm$.First,find the vertical height $(h)$ using the relation $l^2 = r^2 + h^2$.$h = \sqrt{l^2 - r^2} = \sqrt{91^2 - 35^2} = \sqrt{(91 - 35)(91 + 35)} = \sqrt{56 	imes 126} = \sqrt{7056} = 84 \,cm$.The volume $(V)$ of the cone is given by $V = \frac{1}{3} \pi r^2 h$.$V = \frac{1}{3} 	imes \frac{22}{7} 	imes 35 	imes 35 	imes 84 = 22 	imes 35 	imes 5 	imes 84 / 3 = 22 	imes 35 	imes 5 	imes 28 = 107800 \,cm^3$.Since $1000 \,cm^3 = 1 \,litre$,the capacity is $107800 / 1000 = 107.8 \,litres$.

The radius and slant height of a conical vessel are $35 \,cm$ and $91 \,cm$ respectively. What is its capacity in litres (in $.8$)?

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