A right circular cone is exactly fitted insid | vedclass

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Question

(A) The volume of the cube is $V_{cube} = a^3 = 343 \, c.c.$Therefore,the edge length of the cube is $a = \sqrt[3]{343} = 7 \, cm$.Since the cone is f

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(A) The volume of the cube is $V_{cube} = a^3 = 343 \, c.c.$Therefore,the edge length of the cube is $a = \sqrt[3]{343} = 7 \, cm$.Since the cone is fitted inside the cube such that its base touches the edges of one face,the diameter of the base of the cone is equal to the side of the cube,$d = 7 \, cm$. Thus,the radius $r = 3.5 \, cm$.The height of the cone is equal to the side of the cube,$h = 7 \, cm$.The volume of the cone is given by $V_{cone} = \frac{1}{3} \pi r^2 h$.$V_{cone} = \frac{1}{3} 	imes \frac{22}{7} 	imes (3.5)^2 	imes 7$.$V_{cone} = \frac{1}{3} 	imes 22 	imes 12.25 = \frac{269.5}{3} \approx 89.83 \, c.c.$Rounding to the nearest integer,the volume is approximately $90 \, c.c.$

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