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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 cone

So 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 calculation

Number of cones $$=\dfrac{4851}{38.5}=126$$

Therefore, $$126$$ cones are obtained from the metallic sphere.

Mathematics
RS Agarwal
Standard IX

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