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Question
Choose the correct answer of the following question:
A metallic solid sphere of radius 9 cm is melted to form a solid cylinder of radius 9 cm. The height of the cylinder is
Options
12 cm
18 cm
36 cm
96 cm
Solution
We have,
Radius of the solid sphere, R = 9 cm and
Radius of the solid cylinder, r = 9 cm
Let the height of the cylinder be h.
Now,
Volume of the cylinder = volume of the sphere
`=> pi"r"^2"h"=4/3pi"R"^3`
`=> "h" = (4"R"^3)/(3"r"^2)`
`=> "h"=(4xx9xx9xx9)/(3xx9xx9)`
∴ h = 12 cm
Hence, the correct answer is option (a)
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