The volume of the largest right circular cone | vedclass

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(A) To find the volume of the largest right circular cone that can be cut from a cube,the diameter of the base of the cone must be equal to the edge o

Vedclass · Accepted Answer

$19.4$

Vedclass · Answer

(A) To find the volume of the largest right circular cone that can be cut from a cube,the diameter of the base of the cone must be equal to the edge of the cube,and the height of the cone must be equal to the edge of the cube.Given edge of the cube,$a = 4.2 \,cm$.Therefore,the radius of the cone,$r = \frac{a}{2} = \frac{4.2}{2} = 2.1 \,cm$.The height of the cone,$h = a = 4.2 \,cm$.The volume of a cone is given by the formula $V = \frac{1}{3} \pi r^2 h$.Substituting the values: $V = \frac{1}{3} 	imes \frac{22}{7} 	imes (2.1)^2 	imes 4.2$.$V = \frac{1}{3} 	imes \frac{22}{7} 	imes 4.41 	imes 4.2$.$V = \frac{1}{3} 	imes 22 	imes 0.63 	imes 4.2$.$V = 22 	imes 0.21 	imes 4.2$.$V = 4.62 	imes 4.2 = 19.404 \,cm^3$.Rounding to one decimal place,we get $19.4 \,cm^3$.

The volume of the largest right circular cone that can be cut out from a cube of edge $4.2 \,cm$ is (in $cm^3$)

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