A solid piece of iron in the form of a cuboid | vedclass

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Question

(C) Given,dimensions of the cuboid $= 49 \, cm 	imes 33 \, cm 	imes 24 \, cm$.Volume of the cuboid $= 	ext{length} 	imes 	ext{breadth} 	imes 	e

Vedclass · Accepted Answer

$21$

Vedclass · Answer

(C) Given,dimensions of the cuboid $= 49 \, cm 	imes 33 \, cm 	imes 24 \, cm$.Volume of the cuboid $= 	ext{length} 	imes 	ext{breadth} 	imes 	ext{height} = 49 	imes 33 	imes 24 = 38808 \, cm^3$.Let the radius of the sphere be $r$.Volume of the sphere $= \frac{4}{3} \pi r^3$.Since the cuboid is moulded into a sphere,their volumes are equal:$\frac{4}{3} \pi r^3 = 38808$$\frac{4}{3} 	imes \frac{22}{7} 	imes r^3 = 38808$$r^3 = \frac{38808 	imes 3 	imes 7}{4 	imes 22}$$r^3 = 441 	imes 21 = 9261$$r = \sqrt[3]{9261} = 21 \, cm$.Thus,the radius of the sphere is $21 \, cm$.

$A$ solid piece of iron in the form of a cuboid of dimensions $49 \, cm \times 33 \, cm \times 24 \, cm$ is moulded to form a solid sphere. The radius of the sphere is (in $cm$):

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