Answer and Step-by-step explanation:
Let's denote the radius of both the hemisphere and the cylinder as "r". Since the hemisphere and cylinder have equal volume, we can set up the following equation:
Volume of hemisphere = Volume of cylinder
The volume of a hemisphere is given by (2/3)πr^3, and the volume of a cylinder is given by πr^2h, where "h" represents the height of the cylinder.
Substituting these values into the equation, we get:
(2/3)πr^3 = πr^2h
Next, we can cancel out the π and r^2 terms from both sides of the equation:
(2/3)r = h
Therefore, the ratio of the height of the cylinder to the radius of the cylinder is 2/3. This means that the height of the cylinder is 2/3 times the radius of the cylinder.
In summary, the ratio of the height of the cylinder to the radius of the cylinder is 2/3.