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The diameters of the internal and external surfaces of a hollow spherical shell are $6cm$ and $10cm$ respectively. If it is melted and recast into a solid cylinder of diameter $14cm$, find the height of the cylinder.
The diameters of the internal and external surfaces of a hollow spherical shell are $6cm$ and $10cm$ respectively. If it is melted and recast into a solid cylinder of diameter $14cm$, find the height of the cylinder.
CBSE | Class 10 | Exercise 16.1 | Maths | RD Sharma | Surface Areas And Volumes
The diameters of the internal and external surfaces of a hollow spherical shell are $6cm$ and $10cm$ respectively. If it is melted and recast into a solid cylinder of diameter $14cm$, find the height of the cylinder.

As per the question,

Internal diameter of hollow spherical shell $=6cm$

Then, the internal radius of hollow spherical shell $=6/2=3cm=r$

External diameter of hollow spherical shell $=10cm$

Therefore, the external diameter of hollow spherical shell $=10/2=5cm=R$

Diameter of the cylinder $=14cm$

Now, the radius of cylinder $=14/2=7cm$

Assume the height of cylinder be taken as h cm

Now, according to the question we have

Volume of cylinder $=$ Volume of spherical shell

$\pi \times {{r}^{2}}\times h=4/3\pi \times \left( {{R}^{3}}-{{r}^{3}} \right)$

$\pi \times {{7}^{2}}\times h=4/3\pi \times \left( {{5}^{3}}-{{3}^{3}} \right)$

$h=4/3\times 2$

$h=8/3cm$

Therefore, the height of the cylinder $=8/3cm$

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