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Question
From a solid cube of side 7 cm , a conical cavity of height 7 cm and radius 3 cm is hollowed out . Find the volume of the remaining solid.
Solution
Side length of the cube, a = 7 cm
Height of the cone, h = 7 cm
radius, r = 3 cm
Volume of the remaining solid = Volume of the cube − volume of the cone
\[V = a^3 - \frac{1}{3} \pi r^2 h\]
\[V = 7^3 - \frac{1}{3}\pi \left( 3 \right)^2 \times 7\]
\[V = 343 - 66 = 277 {cm}^3\]
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