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The surface area of a solid metallic sphere is 616 cm². It is melted and recast into smaller spheres of diameter 3.5 cm.

How many such spheres can be obtained?

Answer:

**Solution:**

No matter how different the new shape is, when we change one solid shape into another, its volume stays the same. In fact, if we melt a single large sphere into a number of smaller ones, the combined volumes of the smaller ones match the size of the large spherical.

Given surface area of the sphere = 616 cm^{2}

4π R^{2} = 616

4×(22/7)R^{2} = 616

R^{2} = 616×7/4×22

R^{2} = 49

R = 7

Volume of the solid metallic sphere = (4/3)π R^{3}

= (4/3)π x 7^{3}

= (1372/3)π cm^{3}

Diameter of smaller sphere = 3.5 cm

So radius, r = 3.5/2 = 7/4 cm

Volume of the smaller sphere = (4/3)π r^{3}

= (4/3)π (7/4)^{3}

= (343/48) π cm^{3}

Number of spheres made = Volume of the solid metallic sphere/ Volume of the smaller sphere

= (1372/3)π ÷(343/48)π

=1372×48/(3×343)

= 64

**Hence the number of spheres made is 64.**

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