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The minimum slant height (in m) of a con...

The minimum slant height (in m) of a cone having volume `2sqrt(3)` cubic meter is:

A

3

B

9

C

`3sqrt(3)`

D

`sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`V = 1/3 pir^2 h = 2sqrt(3) pi`
`r^2 h = 6sqrt(3)`
`l^2 = r^2 + h^2`
`f(h) = h^2 + (6sqrt3)/(h)`
`f'(h) = 2h-(6sqrt(3))/(h^2) = 0`
`h^3 = 3sqrt(3) implies h = sqrt(3)`
`f(h) = 3 + 6 = 9`
`l = 3m`.
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