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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
From the figure, we get,
Volume of remaining solid = Volume of cube – Volume of cone
For Cube
Side, a = 7 cm
We know that,
Volume of cube = a3, where a = side of cube
Volume of cube = (7)3 = 343 cm3
For cone
Radius, r = 3 cm
Height, h = 7 cm
Volume of cone = `1/3 π"r"^2"h"`
= `1/3 π(3)^(2)7`
= `3 xx 22/7 xx 7`
= 66 cm3
Volume of remaining solid = Volume of cube – Volume of cone
= 343 – 66
= 277 cm3
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