A rectangular block of metal has dimensions 2 | vedclass

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(A) The volume of the rectangular block is given by $V = 	ext{length} 	imes 	ext{breadth} 	imes 	ext{height} = 21 	imes 77 	imes 24 \, cm^3$.Le

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$21$

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(A) The volume of the rectangular block is given by $V = 	ext{length} 	imes 	ext{breadth} 	imes 	ext{height} = 21 	imes 77 	imes 24 \, cm^3$.Let the radius of the sphere be $r \, cm$.Since the block is melted into a sphere, the volume of the sphere must be equal to the volume of the rectangular block.Volume of sphere $= \frac{4}{3} \pi r^3$.Equating the volumes: $\frac{4}{3} 	imes \frac{22}{7} 	imes r^3 = 21 	imes 77 	imes 24$.Solving for $r^3$: $r^3 = \frac{21 	imes 77 	imes 24 	imes 3 	imes 7}{4 	imes 22}$.Simplifying the expression: $r^3 = \frac{21 	imes 77 	imes 24 	imes 21}{88} = \frac{21 	imes 77 	imes 6 	imes 21}{22} = 21 	imes 7 	imes 3 	imes 21 = 21 	imes 21 	imes 21 = 21^3$.Therefore, $r = 21 \, cm$.

$A$ rectangular block of metal has dimensions $21\, cm$, $77\, cm$, and $24\, cm$. The block is melted into a sphere. The radius of the sphere is .......... $cm$. (Take $\pi = \frac{22}{7}$)

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