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.

Answer 1

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