Answer: The volume of a hemisphere is given by the formula:
V = (2/3)πr^3
where V is the volume and r is the radius.
However, in this case, we are given the volume of the hemisphere, not the volume of the full sphere. The volume of a hemisphere is half the volume of the full sphere, so we can find the volume of the full sphere and then use that to find the diameter.
The volume of the full sphere is:
V_sphere = 2V_hemisphere = 2(8582) = 17164 m^3
Using the formula for the volume of a sphere, we can solve for the radius:
V_sphere = (4/3)πr^3
17164 = (4/3)πr^3
r^3 = (3/4)(17164/π)
r ≈ 14.1 m
The diameter of the sphere is twice the radius, so:
d ≈ 2r ≈ 28.2 m
Therefore, the diameter of the hemisphere with a volume of 8582 m^3, rounded to the nearest tenth of a meter, is approximately 28.2 meters.
Explanation: