The statement is true. --- Let the radius of the base of the right circular cone and the hemisphere be \(r\), and their heights be \(h_1\) and \(h_2\) respectively. For the hemisphere, the radius is \(r = h_2\) Therefore, according to the question: \[ \frac{1}{3} \pi r^2 h_1 = \frac{2}{3} \pi r^3 \] or, \[ h_1 = 2r \] or, \[ h_1 = 2h_2 \quad [\because r = h_2] \] or, \[ \frac{h_1}{h_2} = 2 \] Hence, the ratio of heights of the cone and the hemisphere is \(2:1\)