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Nail in Can
Hi All,
A similar question to the ladder one i posted earlier. Now that i have an idea from what i was shown earlier, i've tried to attempt it.
The Question says: A 20cm nail fits inside a cylindrical can. Find the maximum radius of 3 balls that will fit exactly inside the can?
I have drawn the diag to the best of my ability. At first i thought the nail stood upright in the can.
So i the length of the can is 20cm and to fit 3 balls in =
20/6 = radius = 3.33cm (wrong ans)
But, using the help i got from the ladder question, I then thought the nail is probably lying diagonally (AB) and then i tried splitting the diag to make right angel triangles.
*h = Radius
(AO)^2 + h^2 = 10^2 > (AO)^2 + h^2 = 100
(2AO)^2 + (2h)^2 = 20^2 > (4AO)^2 + (4h^2) = 400
Subtracting the two doesn't work..
I tried making (AO^2) the subject = AO^2 = 100  h^2
and sub it into the second equation...still nothing :(

Re: Nail in Can

Re: Nail in Can
Hi Soroban, Thank you! I substituted the above value of [tex]sqrt{10}=\pm 3.16[\math]
into the equation constructed to cross check if i get the correct hypotenuse of 20cm and i obtained 19.98[tex]\simeq[\math] 20.
However, in the textbook the ans is 3.03 and when that is substituted for h = 19.16 , which is a large margin of error, must be an error in the txtbook...
Thank you ;)