The volume of the largest right circular cone | vedclass

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Question

(B) For the largest right circular cone cut from a cube of edge $a = 7 \, cm$:The diameter of the base of the cone $d = a = 7 \, cm$,so the radius $r

Vedclass · Accepted Answer

$89.8$

Vedclass · Answer

(B) For the largest right circular cone cut from a cube of edge $a = 7 \, cm$:The diameter of the base of the cone $d = a = 7 \, cm$,so the radius $r = \frac{7}{2} \, cm$.The height of the cone $h = a = 7 \, cm$.The volume of the cone $V = \frac{1}{3} \pi r^2 h$.Substituting the values: $V = \frac{1}{3} 	imes \frac{22}{7} 	imes (\frac{7}{2})^2 	imes 7$.$V = \frac{1}{3} 	imes \frac{22}{7} 	imes \frac{49}{4} 	imes 7$.$V = \frac{1}{3} 	imes 22 	imes \frac{49}{4} = \frac{11 	imes 49}{6} = \frac{539}{6} \approx 89.83 \, cm^3$.Thus,the volume is approximately $89.8 \, cm^3$.

The volume of the largest right circular cone that can be cut out of a cube of edge $7 \, cm$ is.....$cm^3$

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