Final answer:
To find the volume of the hemisphere, calculate the radius from the circumference of the great circle and then apply the formula for the volume of a sphere, while remembering to use consistent units. For a hemisphere, the volume formula is halved.
Step-by-step explanation:
To determine the volume of the hemisphere, we first need to calculate the radius of the hemisphere using the perimeter of the great circle, which is the same as the circumference of a circle. The formula for the circumference (C) of a circle is C = 2πr, where r is the radius. If the perimeter of the great circle is given as î centimeters, we can set up an equation and solve for r: î = 2πr, which gives us r = î/(2π).
Once we have the radius, we can calculate the volume of the hemisphere. The volume (V) of a sphere is given by the formula V = (4/3)πr³. Since a hemisphere is half of a sphere, we divide this volume by 2. Therefore, the volume of the hemisphere is V = (2/3)πr³. Substituting the value of r we found earlier, the volume formula becomes V = (2/3)π(î/(2π))³.
We should also remember to use consistent units, so if our perimeter was given in another unit of length, it should be converted to centimeters before applying the formulas.