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From a solid cylinder of height $36$ cm and diameter $14$ cm, a conical cavity of radius $7$ cm and height $24$ cm is drilled out. Find the volume of the remaining solid.
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Sol. Radius of cylinder = $7$ cm
Volume of the remaining solid = $\frac{22}{7} \times (7)^2 \times 36 - \frac{1}{3} \times \frac{22}{7} \times (7)^2 \times 24$
= $5544 - 1232$
= $4312 \text{ cm}^3$
Therefore, volume of the remaining solid is $4312 \text{ cm}^3$.
Volume of the remaining solid = $\frac{22}{7} \times (7)^2 \times 36 - \frac{1}{3} \times \frac{22}{7} \times (7)^2 \times 24$
= $5544 - 1232$
= $4312 \text{ cm}^3$
Therefore, volume of the remaining solid is $4312 \text{ cm}^3$.