Final answer:
The volume of a hemisphere with a radius of 5 inches is calculated by first determining the volume of a full sphere using the formula V = (4/3)πr³, and then dividing that by 2. The final volume of the hemisphere is 261.7994 cubic inches.
Step-by-step explanation:
Volume of a Hemisphere
The question involves finding the volume of a hemisphere, which is half of a sphere, with a given radius of 5 inches. First, we would calculate the volume of a full sphere using the formula V = (4/3)πr³, and then divide that by 2 to get the hemisphere volume. Therefore, for a sphere with a radius of 5 inches:
Volume of the sphere, V = (4/3)π × 5³.
Volume of the hemisphere = V/2.
After performing the calculations:
Volume of the sphere, V = (4/3)π × 125 = 523.5988 cubic inches.
Volume of the hemisphere = 261.7994 cubic inches.