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A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm.

Find the number of cones thus obtained.

Answer:

**Solution:**

When we convert one solid shape to another, its volume remains the same, no matter how different the new shape is. In fact, if we melt one big sphere to many small cones, the sum of the volumes of the smaller cones is equal to the volume of the sphere.

Given radius of the metallic sphere, R = 10.5 cm

Volume of the sphere = (4/3)π R^{3}

= (4/3)π 10.5^{3}

= 1543.5 π cm^{3}

Radius of cone, r = 3.5 cm

Height of the cone, h = 3 cm

Volume of the cone = (1/3)π r^{2}h

= (1/3)π x 3.5^{2}×3

= 12.25π cm^{3}

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

= 1543.5π /12.25π

= 126

**Hence the number of cones that can be made is 126.**

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