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Question
A metallic sphere 1 dm in diameter is beaten into a circular sheet of uniform thickness equal to 1 mm. Find the radius of the sheet.
Solution
Radius of metallic sphere `r = 10/2 cm`
Thickness of circular sheet
`h = 1mm`
` = 1/10 cm`
Let r1 be the radius of sheet.
Therefore,
Volume of circular sheet = volume of metallic sphere
`pi r_1^2 xx h = 4/3 pi r^3`
`r_1^2 xx 1/10 = 4/3 xx (5)^3`
`r_1^2 = (4 xx 125 xx 10)/3`
` = (5000)/3`
`r_1 = sqrt(5000)/3`
`r_1 = 40.8 cm`
Hence, the radius of circular sheet = 40.8 cm
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