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प्रश्न
The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 cm3, then find the radius of the base of the cylinder.
उत्तर
Let the radius of the base and the height of the cylinder be r and h, respectively
We have,
r : h = 2 : 3 i.e `"r"/"h" = 2/3`
or `"h" = (3"r")/2` .........(i)
As,
Volume of the cylinder = 12936 cm3
`=> pi"r"^2"h" = 12936`
`=> 22/7xx"r"^2xx(3"r")/2 = 12936` [Using (i)]
`=> 33/7xx"r"^3=129336`
`=> "r"3 = 12936xx7/33`
⇒ r3 = 2744
`=> r = root(3)(2744)`
∴ r = 14 cm
o, the radius of the base of the cylinder is 14 cm.
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