There is a wooden sphere of radius 6 sqrt{3} | vedclass

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(B) For the largest possible cube cut out from a sphere,the diagonal of the cube is equal to the diameter of the sphere.Let the radius of the sphere b

Vedclass · Accepted Answer

$864 	ext{ cm}^2$

Vedclass · Answer

(B) For the largest possible cube cut out from a sphere,the diagonal of the cube is equal to the diameter of the sphere.Let the radius of the sphere be $r = 6 \sqrt{3} 	ext{ cm}$.Diameter of the sphere $D = 2r = 2 	imes 6 \sqrt{3} = 12 \sqrt{3} 	ext{ cm}$.Let the side length of the cube be $a$. The diagonal of a cube is given by $\sqrt{3}a$.Equating the diagonal of the cube to the diameter of the sphere:$\sqrt{3}a = 12 \sqrt{3}$$a = 12 	ext{ cm}$.The surface area of a cube is given by $6a^2$.Surface area $= 6 	imes (12)^2 = 6 	imes 144 = 864 	ext{ cm}^2$.

There is a wooden sphere of radius $6 \sqrt{3} \text{ cm}$. The surface area of the largest possible cube cut out from the sphere will be:

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