a rectangular container with dimensions 10 inches by 15 inches by 20 inches is to be filled with water, using a cylindrical cup whose radius is 2 inches and whose height is 5 inches, what is the maximum number of full cups of water that can be placed in the container without it overflowing?

Calculate the volume of the container:

Vc = 10*15*20 = 3000 in³

Calculate the volume of the cylindrical cup:
Vp= πr²h = π*2²*5 = 62.832 in³

Maximum number of cups without overflow
= 3000/62.832
= 47.75 cups
Therefore, up to 47 cups, the container will not overflow.

Well, this sounds like a water-dry-namics problem! Let's dive into it!

To find the maximum number of full cups that can fit in the container without having a water party, we need to calculate the volume of both the container and the cup.

First, let's find the volume of the container:
Volume = length x width x height
Volume = 10 inches x 15 inches x 20 inches
Volume = 3,000 cubic inches

Now, let's find the volume of the cylindrical cup:
Volume = Pi x radius^2 x height
Volume = 3.14 x 2 inches x 2 inches x 5 inches
Volume = 62.8 cubic inches

To find out the number of cups that can fit inside the container, we'll just divide the volume of the container by the volume of one cup:

Number of cups = Volume of container / Volume of one cup
Number of cups = 3,000 cubic inches / 62.8 cubic inches
Number of cups ≈ 47.79

Since we can't have a fraction of a cup (unless we were attending a circus-themed tea party), the maximum number of FULL cups would be 47.

So, it looks like you can fit 47 full cups of water in the container without causing a liquid catastrophe!

To find the maximum number of full cups of water that can be placed in the container without it overflowing, we need to calculate the volume of the container and the volume of one cylindrical cup.

1. Calculate the volume of the container:
Volume = Length x Width x Height
Volume = 10 inches x 15 inches x 20 inches
Volume = 3000 cubic inches

2. Calculate the volume of one cylindrical cup:
Volume = π x Radius^2 x Height
Volume = 3.14 x (2 inches)^2 x 5 inches
Volume = 3.14 x 4 square inches x 5 inches
Volume = 62.8 cubic inches

3. Divide the volume of the container by the volume of one cylindrical cup to find the maximum number of full cups that can fit without overflowing:
Maximum number of cups = Volume of container / Volume of one cup
Maximum number of cups = 3000 cubic inches / 62.8 cubic inches (rounded down)
Maximum number of cups = 47.77
Therefore, the maximum number of full cups of water that can be placed in the container without it overflowing is 47.

To find the maximum number of full cups of water that can be placed in the container without it overflowing, we need to determine how many cups can fit in each dimension and then multiply the results.

First, let's figure out how many cups can fit in terms of width. The width of the container is 10 inches, while the diameter of the cup is 4 inches (twice the radius). The cup cannot fit widthwise, as 4 inches is greater than 10 inches.

Next, let's consider the length of the container. The length is 15 inches, which is less than twice the cup's diameter (8 inches). Thus, the cup can fit lengthwise.

Now, we need to determine how many cups can fit in terms of height. The height of the container is 20 inches, while the height of the cup is 5 inches. 20 divided by 5 equals 4. So the cup can fit 4 times in terms of height.

Since the cup can fit once lengthwise and four times heightwise, the maximum number of cups that can fit in the container is 1 x 4 = 4 cups.