I am solving a related rates problem and it is saying if a cone has a fixed slant height what radius and height would maximize the volume? Exact question: "Among all right circular cones with a slant height of 12, what are the dimensions​ (radius and​ height) that maximize the volume of the cone? The slant height of a cone is the distance from the outer edge of the base to the vertex." I tried filling the volume for the cone equation with the Pythagorean theorem for the height but still got the answer wrong. How would I go about solving this?

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