Question
A solid metallic sphere of radius $5.6\ cm$ is melted and solid cones each of radius $2.8\ cm$ and height $3.2\ cm$ are made. Find the number of such cones formed.
✓
Answer
Let the number of such cones formed be $n$
Now, volume of solid metallic sphere = volume of n solid cones
$\Rightarrow\frac{4}{3}\times\frac{22}{7}\times(5.6)^3=\text{n}\times\frac{1}{3}\times\frac{22}{7}\times(2.8)^2\times3.2$
$\Rightarrow4\times(5.6)^3=\text{n}\times(2.8)^2\times3.2$
$\Rightarrow\text{n}=28$
Now, volume of solid metallic sphere = volume of n solid cones
$\Rightarrow\frac{4}{3}\times\frac{22}{7}\times(5.6)^3=\text{n}\times\frac{1}{3}\times\frac{22}{7}\times(2.8)^2\times3.2$
$\Rightarrow4\times(5.6)^3=\text{n}\times(2.8)^2\times3.2$
$\Rightarrow\text{n}=28$
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