Final answer:
To determine the weight of ice cream that can fit in the cone, calculate the volume of the ice cream by using the formula for the volume of a hemisphere. Then, use the given information about the weight of ice cream per cubic foot to find the weight of the ice cream that can fit in the cone.
Step-by-step explanation:
To determine the weight of ice cream that can fit in the cone, we need to calculate the volume of the ice cream. The shape of the ice cream above the cone is a perfect hemisphere. The formula to calculate the volume of a hemisphere is (2/3)πr³, where r is the radius of the hemisphere.
Given that the diameter of the cone's rim is 2 inches, the radius (r) of the hemisphere is 1 inch. Substituting this value into the volume formula, we get:
Volume = (2/3)π(1 inch)³ = (2/3)π cubic inches.
Now we can use the given information that a gallon of ice cream occupies 7.5 cubic feet and weighs 8 lbs. Since there are 12 inches in a foot, 1 cubic foot is equal to 12³ = 1728 cubic inches. Therefore, 7.5 cubic feet is equal to 7.5 x 1728 cubic inches. To find the weight of ice cream that can fit in the cone, we need to find the weight of (2/3)π cubic inches of ice cream:
Weight = (8 lbs / 7.5 cubic feet) * (7.5 cubic feet * 1728 cubic inches) * [(2/3)π cubic inches / 1728 cubic inches].
Calculating this expression will give us the weight of ice cream that can fit in the cone.