From a solid cube of side 7 , cm,a conical ca | vedclass

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(A) Given that,the side of the solid cube $(a) = 7 \, cm$.The height of the conical cavity (cone),$h = 7 \, cm$.The radius of the conical cavity (cone

Vedclass · Accepted Answer

$277$

Vedclass · Answer

(A) Given that,the side of the solid cube $(a) = 7 \, cm$.The height of the conical cavity (cone),$h = 7 \, cm$.The radius of the conical cavity (cone),$r = 3 \, cm$.Volume of the cube $= a^3 = (7)^3 = 343 \, cm^3$.Volume of the conical cavity (cone) $= \frac{1}{3} \pi r^2 h = \frac{1}{3} 	imes \frac{22}{7} 	imes (3)^2 	imes 7$.$= \frac{1}{3} 	imes 22 	imes 9 = 66 \, cm^3$.Volume of the remaining solid $=$ Volume of the cube $-$ Volume of the conical cavity.$= 343 - 66 = 277 \, cm^3$.Thus,the volume of the remaining solid is $277 \, cm^3$.

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 (in $cm^3$).

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