a metallic sphere of radius 8.4 cm is melted and recast into the shape of a cylinder of radius 4 cm so that the height of the cylinder is 49.4 CM
Answers
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If the sphere of radius 8.4 cm is reformed into a cylinder of radius 4 cm then it is proved that the height of the cylinder is 49.4 cm.
Step-by-step explanation:
The radius of the metallic sphere, r₁ = 8.4 cm
The radius of the cylinder, r₂ = 4 cm
Let the height of the cylinder be denoted as “h” cm.
Since the sphere is melted and recast into the shape of a cylinder
Therefore,
[The volume of the sphere] = [The volume of the cylinder]
⇒ [4/3 * π * r₁³] = [π * r₂² * h]
⇒ [4/3 * (22/7) * (8.4)³] = [(22/7) * (4)² * h]
⇒ [4/3 * (8.4)³] = [(4)² * h]
⇒ [790.272] = [16 * h]
⇒ h = 49.39
⇒ h ≈ 49.4 cm ← the height of the cylinder
Hence proved
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