Question

# A metallic sphere of radius $$10.5cm$$ is melted and then recast into smaller cone, each of radius $$3.5cm$$ and height $$3cm$$. How many cones are obtained?

Solution

## It is given that Radius of the sphere $$=10.5cm$$Radius of smaller cone $$=3.5cm$$Height $$=3cm$$We know that Number of cones = Volume of the sphere $$\div$$ Volume of one small coneSo we get Number of cones $$=\dfrac{\left(\dfrac{4}{3} \times \dfrac{22}{7}\times (10.5)^3\right)}{\left(\dfrac{1}{3} \times \dfrac{22}{7}\times 3.5^2 \times 3\right)}$$On further calculationNumber of cones $$=\dfrac{4851}{38.5}=126$$Therefore, $$126$$ cones are obtained from the metallic sphere.MathematicsRS AgarwalStandard IX

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