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प्रश्न
The diameters of internal and external surfaces of hollow spherical shell are 10cm and 6cm respectively. If it is melted and recast into a solid cylinder of length of 2`2/3`cm, find the
diameter of the cylinder.
उत्तर
Given diameter of internal surfaces of a hollow spherical shell = 10cm
Radius (r)`=10/2=5cm`
External radii (R)`=6/2=3cm`
Volume of a spherica shell (hollow) =`4/3pi(R^2-r^2)`
`V_1=4/3pi(5^2-3^2)cm^3` ........(1)
Given length of solid cylinder `(h)=8/3`
Let radius of solid cylinder be 'r'
Volume of a cylinder `pir^2h`
`V_2=pir^2(8/3)cm^3` .........(2)
V1 = V2
Equating (1) and (2)
⇒`4/3pi(25-9)=pir^2(8/3)`
⇒`(4/3pi(16))/(pi(8/3))=r^2`
⇒ r2 = 49cm
⇒ r = 7cm
d = 2r = 14cm
∴ Diameter of cylinder = 14cm
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