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प्रश्न
The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.
उत्तर
Internal diameter of hollow spherical shell = 6cm
Internal radius of hollow spherical shell =`6/3=3` cm
External diameter of hollow spherical shell = 10 cm
External radius of hollow spherical shell = `10/2=5`cm
Diameter of cylinder = 14 cm
Radius of cylinder`=14/2=7`cm
Let height of cylinder = xcm
According to the question
Volume of cylinder = Volume of spherical shell
⇒ `pi(7)^2x xx=4/3pi(5^3-3^3)`
⇒`49x xx=4/3(125-27)`
⇒`49x xx=4/3xx98`
`x=(4xx98)/(3xx49)=8/3cm`
∴Height off cylinder=`8/3cm`
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