A paper cup is the shape of a cone with a height of 12 cm and radius 4 cm at the top. Water is poured into he cup at a rate of 2cm^3/s. How fast is the water level rising when the water level is 8 cm deep?

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A paper cup is the shape of a cone with a height of 12 cm and radius 4 cm at the top. Water is poured into he cup at a rate of 2cm^3/s. How fast is the water level rising when the water level is 8 cm deep?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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V = pi r^2 h / 3 dV = (pi/3)*(2rdr + r^2 * dh) since h/12 = r/4 r =h/3 and dr =dh/3 dV/dt =(pi/3)*(2(h/3)((dh/dt)/3) + (h/3)^2 * dh/dt) dV/dt = 2 and h = 8 2 =(pi/3)*(2(8/3)((dh/dt)/3) + (8/3)^2 * dh/dt) solve for dh/dt
maybe I'm working it out wrong but the sheet says that I should get 9/32pi for the answer and instead I'm getting 27/56pi

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