A container in the shape of a rectangle solid with the dimensions of 4 X 5 X10 is placed so that its height is 10. Water fills the container to a heaight of 6. The container is then turned so that the base dimensions are 4 X 10. Determine the height of the water in the container.
4x5x6 = 4x10xh
120 = 40h
h = 3
To determine the height of the water in the container after it is turned, we can use the principle of conservation of volume.
First, let's calculate the volume of the original container. The formula to calculate the volume of a rectangular solid (or rectangular prism) is V = l × w × h, where l, w, and h are the length, width, and height of the solid, respectively.
In this case, the original container has dimensions of 4 x 5 x 10. So, the volume is V = 4 × 5 × 10 = 200 cubic units.
Next, let's calculate the height of the water when the container is turned.
Since the base dimensions are now 4 x 10, the area of the base is A = l × w = 4 × 10 = 40 square units.
To determine the height of the water, we can divide the original volume of the container (200 cubic units) by the current base area (40 square units). This gives us:
height of water = original volume / current base area
= 200 / 40
= 5 units.
Therefore, the height of the water in the container when it is turned with a base dimensions of 4 x 10 would be 5 units.