Let the common base radius be \( r \) and the height be \( h \). Since a hemisphere's height is equal to its radius, we have \( h = r \) for all three objects. Volume of Cylinder = \( \pi r^2 h = \pi r^2 (r) = \pi r^3 \) Volume of Cone = \( \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi r^3 \) Volume of Hemisphere = \( \frac{2}{3} \pi r^3 \) The ratio of their volumes (Cylinder : Cone : Hemisphere) is: \[ \pi r^3 : \frac{1}{3} \pi r^3 : \frac{2}{3} \pi r^3 \] Divide the entire ratio by \( \pi r^3 \): \[ 1 : \frac{1}{3} : \frac{2}{3} \] Multiply by 3 to clear the fractions: \[ 3 : 1 : 2 \]