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Answer in Brief

The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.

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#### Solution

The radius of the largest possible cone is carved out of a solid cube is equal to the half of the side of the cube.

Also, the height of the cone is equal to the side of the cube.

Radius of the cone = \[\frac{21}{2} = 10 . 5\]

Volume of the remaining solid = Volume of cube − Volume of cone

\[= \left( \text { Side } \right)^3 - \frac{1}{3}\pi r^2 h\]

\[ = \left( 21 \right)^3 - \frac{1}{3} \times \frac{22}{7} \times \left( 10 . 5 \right)^2 \times 21\]

\[ = 9261 - 2425 . 5\]

\[ = 6835 . 5 {cm}^3\]

**Disclaimer**: The answer given in the book is not correct.

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