### Instruction: Brad has a cylindrical barrel with radius 10 inches and height 15 inches.  He wants to fill it from a well, using a bucket in the shape of a hemisphere with a radius of 10 inches. How many trips must Brad make to the well in order to fill the barrel?### Response: To fill the barrel, Brad needs to transfer the same volume of water from the bucket to the barrel.
The volume of the cylindrical barrel is given by the formula V = pi * r^2 * h, where r is the radius and h is the height.
Plugging in the given values, I get V = pi * 10^2 * 15 = 1500 pi cubic inches.
The volume of the hemispherical bucket is half of the volume of a full sphere, which is given by the formula V = 4/3 * pi * r^3, where r is the radius.
Plugging in the given values, I get V = 4/3 * pi * 10^3 / 2 = 2000 pi / 3 cubic inches.
To find the number of trips Brad needs to make, I need to divide the volume of the barrel by the volume of the bucket, and round up to the nearest integer.
This gives me N = ceil(1500 pi / (2000 pi / 3)) = ceil(9/4) = 3.
Therefore, Brad needs to make 3 trips to the well to fill the barrel.