Question:
A solid metal sphere of 6 cm diameter is melted and a circular sheet of thickness 1 cm is prepared. Determine the diameter of the sheet.
Solution:
Diameter of sphere = 6 cm
Therefore,
Radius = 3 cm.
Therefore,
Surface area of sphere
$=4 \pi r^{2}$
$=4 \times \pi \times(3)^{2}$
$=36 \pi \mathrm{cm}^{2}$
Area of the circular sheet $=\pi r^{2}$
Therefore,
Surface area of sphere = area of the circular sheet
$r=6 \mathrm{~cm}$
Therefore,
Diameter of the sheet = 2 × 6 = 12 cm
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