The Largest Cone Is Curved Out From One Face Of Solid Cube Of Side 21cm. Find The Volume Of The Remaining Solid.

Sol:

Let the maximum volume of the cone that can be carved will be of radius = 0.5 side length of cube.

Radius, R = 0.5L

= 0.5 * 21

= 10.5 cm

Given = 21cm.

V = \(\frac{1}{3}\Pi R^{2}h \\\Rightarrow \frac{1}{3}\Pi * (10.5)^{2} * 21\\\Rightarrow2424.52 cm^{3}\)

The volume of wood left = Volume of the cube – V.

\(\Rightarrow V1 = 1^{3} – V = 21^{3} – 2424.52\\\Rightarrow 21^{3} – 2424.52\\\Rightarrow 6836.5 cm^{3}\)

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