The volume of the shapes must be equal thus, \(V_{cy} = V_{fcone}\)

Volume of the cylinder: \(V_{cy} = \pi r^2h\)

\(V_{cy} = \pi (1)^2 (3)\)

\(V_{cy} = 3\pi \)

Volume of the frustum of a cone: \(V_{fc} = \frac{1}{3} \pi h (r_1^2 + r_2^2 + r_1r_2)\)

\(V_{fc} = \frac{1}{3} \pi h ((0.5)^2 + (1)^2 +(0.5)(1))\)

\(V_{fc} = \frac{7}{12}\pi h\)

\(3\pi = \frac{7}{12}\pi h\)

\(h = 5.14 ~ m\)