A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.


Answer :


Volume of the sphere \( = \ \frac{4}{3} \pi r^3 \ = \ \frac{4}{3} \ × \ \pi \ × \ (4.2)^3 \) cm3

If h is the height of a cylinder of radius 6 cm. Then its volume \(= \ \pi (6)^2 h \ = \ 36\pi h \) cm3

\(\therefore \) The volume of metal in the form of sphere and cylinder remains the same , we have

\(\Rightarrow 36 \pi h \ = \ \frac{4}{3} \ × \ \pi \ × \ (4.2)^3 \)

\(\Rightarrow \ h \ = \ \frac{1}{36} \ × \ \frac{4}{3} \ × \ (4.2)^3 \)

\( \Rightarrow \ h \ = \ 2.744 \) cm

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