A metal sphere of radius 20, cm is melted and | vedclass

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(C) The volume of the large sphere of radius $R = 20\, cm$ is given by $V_s = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (20)^3 = \frac{4}{3} \pi (8000)\,

Vedclass · Accepted Answer

$128$

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(C) The volume of the large sphere of radius $R = 20\, cm$ is given by $V_s = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (20)^3 = \frac{4}{3} \pi (8000)\, cm^3$.The volume of one small hemisphere of radius $r = 5\, cm$ is given by $V_h = \frac{2}{3} \pi r^3 = \frac{2}{3} \pi (5)^3 = \frac{2}{3} \pi (125)\, cm^3$.The number of hemispheres $n$ is given by the ratio of the volume of the sphere to the volume of one hemisphere:$n = \frac{V_s}{V_h} = \frac{\frac{4}{3} \pi (8000)}{\frac{2}{3} \pi (125)} = \frac{4 	imes 8000}{2 	imes 125} = \frac{32000}{250} = 128$.Thus,the total number of hemispheres obtained is $128$.

$A$ metal sphere of radius $20\, cm$ is melted and then cast into small hemispheres each of radius $5\, cm$. Find the number of hemispheres thus obtained (in balls).

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