A cube of side 4 , cm contains a sphere touch | vedclass

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(B) Side of the cube $a = 4 \, cm$.Volume of the cube $V_{cube} = a^3 = (4)^3 = 64 \, cm^3$.Since the sphere touches the sides of the cube,the diamete

Vedclass · Accepted Answer

$30.48$

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(B) Side of the cube $a = 4 \, cm$.Volume of the cube $V_{cube} = a^3 = (4)^3 = 64 \, cm^3$.Since the sphere touches the sides of the cube,the diameter of the sphere is equal to the side of the cube,$d = 4 \, cm$.Radius of the sphere $r = d / 2 = 4 / 2 = 2 \, cm$.Volume of the sphere $V_{sphere} = \frac{4}{3} \pi r^3 = \frac{4}{3} 	imes \frac{22}{7} 	imes (2)^3$.$V_{sphere} = \frac{4}{3} 	imes \frac{22}{7} 	imes 8 = \frac{704}{21} \approx 33.52 \, cm^3$.Volume of the gap = $V_{cube} - V_{sphere} = 64 - 33.52 = 30.48 \, cm^3$.

$A$ cube of side $4 \, cm$ contains a sphere touching its sides. Find the volume of the gap in between. (in $, cm^3$)

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