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प्रश्न
A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell.
उत्तर
External radius of spherical shell
`r_1 = 18 /2 = 9 cm`
Let r2 be the internal radius of spherical shell.
Height of right circular cylinder h = 8 cm
& radius of right circular cylinder
`r = 12 /2 = 6 cm`
Clearly, volume of spherical shell = volume of right circular cylinder
`4/3 pi (r_1^3 - r_2^3 ) = pi r^2 h`
`4/3(9^3 - r_2^3) = (6)^2 xx 8`
`729 - r_3^2 = (36^9 xx 8 xx 3)/4`
`729 - r_2^3 = 216`
` r_2^3 = 513`
` r_2 = 3sqrt513`
` r_2 = 3(19)^(1/3) cm`
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