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(D) The side of the cube is $a = 7 \ cm$.Volume of the cube $= a^3 = 7^3 = 343 \ cm^3$.The largest cone inscribed in the cube will have a base diamete

Vedclass · Accepted Answer

$11:42$

Vedclass · Answer

(D) The side of the cube is $a = 7 \ cm$.Volume of the cube $= a^3 = 7^3 = 343 \ cm^3$.The largest cone inscribed in the cube will have a base diameter equal to the side of the cube and a height equal to the side of the cube.Radius of the cone $(r) = \frac{a}{2} = \frac{7}{2} = 3.5 \ cm$.Height of the cone $(h) = a = 7 \ cm$.Volume of the cone $= \frac{1}{3} \pi r^2 h = \frac{1}{3} 	imes \frac{22}{7} 	imes (3.5)^2 	imes 7 = \frac{1}{3} 	imes 22 	imes 12.25 = \frac{269.5}{3} \approx 89.83 \ cm^3$.Ratio of the volume of the cone to the volume of the cube $= \frac{\frac{1}{3} \pi r^2 h}{a^3} = \frac{\frac{1}{3} 	imes \frac{22}{7} 	imes (\frac{7}{2})^2 	imes 7}{7^3} = \frac{\frac{1}{3} 	imes \frac{22}{7} 	imes \frac{49}{4} 	imes 7}{343} = \frac{\frac{1}{3} 	imes 22 	imes \frac{49}{4}}{343} = \frac{11 	imes 49}{6 	imes 343} = \frac{11}{6 	imes 7} = \frac{11}{42}$.Thus,the ratio is $11:42$.

The largest cone is formed at the base of a cube of side measuring $7 \ cm$. Find the ratio of the volume of the cone to the volume of the cube.

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