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From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. What is the volume of the remaining solid?

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277 cm³

230 cm³

451 cm³

555 cm³

answer is A.

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Detailed Solution

Given that from a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out.
Now the volume of remaining solid = volume of a cube - volume of a conical cavity. So,

V = a^{3} - \frac{1}{3} π r^{2} h

\Rightarrow {(7)}^{3} - \frac{1}{3} (\frac{22}{7}) {(3)}^{2} (7)

\Rightarrow 343 - 66

\Rightarrow 277 {cm}^{3}

Therefore, the correct option is 1.

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