Answer:
To calculate the percentage of the rectangular prism that will be filled with water, we need to compare the volume of water to the volume of the prism.
First, let's calculate the volume of the rectangular prism. The volume of a rectangular prism is given by the formula:
Volume = Height * Width * Length
In this case, the height is 1.00 in, the width is 2.00 in, and the length is 2.00 in. So the volume of the rectangular prism is:
Volume_prism = 1.00 in * 2.00 in * 2.00 in = 4.00 in³
Next, let's calculate the volume of the water in the cylindrical container. The volume of a cylinder is given by the formula:
Volume_cylinder = π * (radius)² * height
In this case, the height of the cylindrical container is 2.00 in, and the diameter (which is twice the radius) is 1.00 in. So the radius is 1.00 in / 2 = 0.50 in. Plugging in the values, we get:
Volume_cylinder = π * (0.50 in)² * 2.00 in ≈ 1.57 in³
Finally, we can calculate the percentage of the rectangular prism that will be filled with water by taking the ratio of the volume of water to the volume of the prism and multiplying by 100:
Percentage_filled = (Volume_cylinder / Volume_prism) * 100
Plugging in the values we calculated, we have:
Percentage_filled = (1.57 in³ / 4.00 in³) * 100 ≈ 39.25%
Therefore, approximately 39.25% of the rectangular prism will be filled with water.
Explanation: