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Question: picture a cone that has as its base the circle...

Question details

Picture a cone that has as its base the circle x^2 + y^2 = r^2 and whose peak is the point z = k: r and k are positive numbers.

Find the formula for the volume of the cone using a double integral over region R = {x^2 + y^2 = r^2}, in polar coordinates.

Then find the same formula by taking slices of the cone perpendicular to the z-axis and integrating the area of those slices from z = 0 to z = k.

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