the ration of cylinder and hemisphere volumes are

Question

the heights of a cone, cylinder and hemisphere are equal. if there radii are in the ratio 2:3:1, then the ratio of their volumes is

Answer 1

If H is the height of the three shapes then their volumes are: (pi)r^2H/3 (cone), (pi)r^2H (cylinder), 2(pi)H^3/3 (hemisphere). In the case of the hemisphere H=radius. We can remove (pi) as the common factor: r^2H/3, r^2H, 2H^3/3. The radius of the cone is 2H because the ratio of the radius of the cone to the radius of the hemisphere is 2:1. The radius of the cylinder is 3H. The volumes are: 4H^3/3, 9H^3, 2H^3/3. Take out the common factor H^3: 4/3, 9, 2/3. Multiply by 3 to get rid of the fractions: 4, 27, 2. So the ratios are 4:27:2. This can be written: 2:13.5:1.