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A certain number of metallic cones each of radius 2 cm and height 3 cm are melted and recast in a solid sphere of radius 6 cm.

Find the number of cones.

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, the volume of the cone is equal to the sum of the volumes of the smaller spheres formed by melting a single large cone into several smaller spheres.

Given radius of metallic cones, r = 2 cm

Height of cone, h = 3 cm

Volume of cone = (1/3)π r^{2}h

= (1/3)π x 2^{2}×3

= 4 π cm^{3}

Radius of the solid sphere, R = 6 cm

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

= (4/3)6^{3}

= 4π x 2×6×6

= 288π cm^{3}

Number of cones made from sphere = Volume of solid sphere / volume of the cone

= 288π /4π

= 72

**Hence the number of cones that can be made is 72.**

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