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(D) Since the spheres are made of the same metal,their density $ho$ is constant. The weight $W$ of a sphere is given by $W = 	ext{Volume} 	imes

Vedclass · Accepted Answer

$5$

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(D) Since the spheres are made of the same metal,their density $ho$ is constant. The weight $W$ of a sphere is given by $W = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi r^3 ho$.Thus,the ratio of weights is equal to the ratio of the cubes of their radii: $\frac{W_1}{W_2} = \frac{r_1^3}{r_2^3}$.Given $W_1 = 5920\, g$ and $W_2 = 740\, g$,we have $\frac{5920}{740} = \frac{r_1^3}{r_2^3}$.Simplifying the ratio: $8 = \frac{r_1^3}{r_2^3}$,which implies $\frac{r_1}{r_2} = \sqrt[3]{8} = 2$.The diameter of the smaller sphere is $5\, cm$,so its radius $r_2 = \frac{5}{2} = 2.5\, cm$.Therefore,the radius of the larger sphere is $r_1 = 2 	imes r_2 = 2 	imes 2.5 = 5\, cm$.

Two solid spheres made of the same metal have weights $5920\, g$ and $740\, g$ respectively. Determine the radius of the larger sphere,if the diameter of the smaller one is $5\, cm$. (in $cm$)

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