Final answer:
The volume of a hemisphere with a radius of 8 units is calculated using half the formula for the volume of a sphere (4/3)πr³, which results in 1072.3 cubic units, corresponding to option A.
Step-by-step explanation:
To calculate the volume of a hemisphere with a radius of 8 units, we need to use the formula for the volume of a sphere and then divide it by two. The formula for the volume of a sphere is V = (4/3)πr³.
First, we'll calculate the volume of a full sphere:
- V = (4/3)π(8³)
- V = (4/3)π(512)
- V = (4/3)(3.1415927)(512)
- V = 2144.6608...
Since this is the volume of a full sphere, we need to divide it by 2 for a hemisphere:
- V_hemisphere = V_sphere / 2
- V_hemisphere = 2144.6608... / 2
- V_hemisphere = 1072.3304...
To find the volume of a hemisphere, we can use the formula:
V = (2/3)πr³
where r represents the radius of the hemisphere.
Given that the radius is 8 units, we can substitute this value into the formula:
V = (2/3)π(8)³ = (2/3)(3.1415927...)(512) ≈ 1071.4 cubic units
Therefore, the correct answer is 1071.4 cubic units (option A).