Mensuration-63

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The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively.
It is melted and recast into a solid circular cylinder of height 10-2/3 cm. Find the radius of the base of the cylinder.

Solution: Let the radius of the base of the cylinder be r,

Therefore, Volume of the right circular cylinder = Π r² h

Here, height h = 10-2/3 cm = 32/3 cm

Hence, Volume of the right circular cylinder

= 22 / 7 x r² x 32/3 cm²

Volume of the spherical shell = 4 Π / 3 {R₂³ - R₁³}

[where, R₂ is the outer radius and R₁ is the inner radius of the spherical shell]

= 4 Π /3 {5³ - 3³} = 4/3 x 22/7 x (125 - 27) = 4/3 x 22/7 x 98 cm³

Now, 22/7 x r² x 32/3 = 4/3 x 22/7 x 98

=> r² = 4/3 x 98 x 3/32

=> r² = 12.25

=> r = 3.5 cm

Hence, the radius of the base of the cylinder is 3.5 cm