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Home » The diameters of the internal and external surfaces of a hollow spherical shell are and respectively. If it is melted and recast into a solid cylinder of diameter , 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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