### Instruction: How many congruent 4-foot tall cylindrical pipes with an inside diameter of 2 inches are needed to hold the same amount of water as one pipe of the same height with an inside diameter of 12 inches?### Response: To compare the amounts of water that different pipes can hold, I need to find the volumes of the pipes.
The volume of a cylinder is given by the formula V = pi * r^2 * h, where r is the radius and h is the height.
The inside diameter of a pipe is twice the inside radius, so I can divide the diameter by 2 to get the radius.
For the smaller pipes, the inside radius is 2/2 = 1 inch, and the height is 4 feet = 48 inches. So the volume of one smaller pipe is V = pi * 1^2 * 48 = 48 pi cubic inches.
For the larger pipe, the inside radius is 12/2 = 6 inches, and the height is also 48 inches. So the volume of the larger pipe is V = pi * 6^2 * 48 = 1728 pi cubic inches.
To find how many smaller pipes are needed to hold the same amount of water as the larger pipe, I need to divide the volume of the larger pipe by the volume of one smaller pipe.
This gives me 1728 pi / 48 pi = 36.
Therefore, I need 36 congruent smaller pipes to hold the same amount of water as one larger pipe.