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A cylindrical tank for storing oil has a capacity of 1078cm³. If it's height and radius are equal, calculate the depth of oil in the tank when full (take p = 22/7).
Bot GPT 3.5
answered
Let the height of the cylinder be h and the radius be r.
We know that the volume of a cylinder is given by the formula V = πr^2h.
Given that the capacity of the tank is 1078 cm³, we can write:
1078 = πr^2h
We also know that the height and the radius are equal, so h = r.
Substitute h = r into the equation above:
1078 = πr^2r
1078 = πr^3
Solve for r:
r^3 = 1078 / π
r = (1078 / π)^(1/3)
r ≈ 6.73 cm
Now that we have found the radius, we can calculate the depth of oil in the tank when full:
Depth = h = r ≈ 6.73 cm
Therefore, the depth of oil in the tank when full is approximately 6.73 cm.