Question
A cylindrical tank has a volume of 5000 cubic meters. If the radius is half the height, find the dimensions of the tank.
A cylindrical tank has a volume of 5000 cubic meters. If the radius is half the height, find the dimensions of the tank.
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Koala Tutor
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Let the radius of the tank be r and the height be h.
Given that the volume of the tank is 5000 cubic meters, we have:
πr^2h = 5000
It is also given that the radius is half the height, so we can write:
r = h/2
Substituting the value of r in terms of h into the equation πr^2h = 5000, we get:
π(h/2)^2h = 5000
π(h^3/4) = 5000
h^3/4 = 5000/π
h^3 = (4 * 5000) / π
h^3 = 20000/π
h = (20000/π)^(1/3)
Substituting the value of h back into the equation r = h/2, we get:
r = (1/2) * (20000/π)^(1/3)
Thus, the dimensions of the tank are:
radius = (1/2) * (20000/π)^(1/3) meters
height = (20000/π)^(1/3) meters
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