Final answer:
To determine the radius of a hemisphere with a volume of 91358 in³, we use the formula for the volume of a sphere and solve for the radius. The calculated radius of the hemisphere is approximately 43.6 inches to the nearest tenth of an inch.
Step-by-step explanation:
To find the radius of a hemisphere with a given volume, we use the formula for the volume of a sphere and then divide the volume by 2, since a hemisphere is half of a full sphere. The formula for the volume of a sphere is V = (4/3)πr^3. Therefore, for a hemisphere, the formula becomes V = (2/3)πr^3. Given that the volume V of the hemisphere is 91358 in³, we can rearrange the formula to solve for r (radius).
First, we isolate r:
V = (2/3)πr^3
r^3 = (3V)/(2π)
r = ((3V)/(2π))1/3
Next, we substitute the given volume into our equation:
r = ((3×91358 in³)/(2π))1/3
r ≈ ((3×91358)/(6.2832))1/3
r ≈ ((274074)/(6.2832))1/3
r ≈ 43.6 in
The radius of the hemisphere is approximately 43.6 inches, when rounded to the nearest tenth of an inch.