From a cubical block of wood of side 1 , m,a | vedclass

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(A) The volume of the cubical block of side $1 \, m$ is $V_{cube} = (1)^3 = 1 \, m^3$.For a cylinder of the largest possible volume carved from this c

Vedclass · Accepted Answer

$\frac{3}{14}$

Vedclass · Answer

(A) The volume of the cubical block of side $1 \, m$ is $V_{cube} = (1)^3 = 1 \, m^3$.For a cylinder of the largest possible volume carved from this cube,the diameter of the base must be equal to the side of the cube ($d = 1 \, m$,so radius $r = 0.5 \, m$) and the height must be equal to the side of the cube $(h = 1 \, m)$.The volume of the cylinder is $V_{cylinder} = \pi r^2 h = \pi 	imes (0.5)^2 	imes 1 = \frac{\pi}{4} \, m^3$.Taking $\pi \approx \frac{22}{7}$,the volume of the cylinder is $V_{cylinder} = \frac{22}{7 	imes 4} = \frac{11}{14} \, m^3$.The volume of the remaining wood is $V_{remaining} = V_{cube} - V_{cylinder} = 1 - \frac{11}{14} = \frac{3}{14} \, m^3$.

From a cubical block of wood of side $1 \, m$,a cylinder of the largest possible volume is carved out. The volume (in $m^3$) of the remaining wood is

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