Final answer:
The volume of the hemisphere with a radius of 9 centimeters is 1526.8 cubic centimeters.
Step-by-step explanation:
To find the volume of the hemisphere with a radius of 9 centimeters, we use the formula for the volume of a sphere and then divide it by 2, because a hemisphere is half of a sphere. The volume V of a sphere is given by V = (4/3)πr³, where r is the radius.
Therefore, the volume of the hemisphere is V = ½ × (4/3)πr³. Plugging in the given radius:
V_hemisphere = ½ × (4/3)π × (9 cm)³
V_hemisphere = ½ × (4/3) × 3.1416 × 729 cm³
V_hemisphere = ½ × (4× 3.1416 × 243)
V_hemisphere = ½ × 3053.6288 cm³
V_hemisphere = 1526.8144 cm³
When rounded to the nearest tenth, the volume of the hemisphere is 1526.8 cm³.