SOLUTION: A rectangular prism with a 6"x6" square base is tilted leftward at a 30<sup>o</sup> angle, It contains water just up to the bottom right corner. How many cubic inches of water d

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Question 1180628: A rectangular prism with a 6"x6" square base is tilted leftward at a 30o
angle, It contains water just up to the bottom right corner. How many cubic
inches of water does it contain?
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


62.35 square inches, to 2 decimal places.

To get that answer, observe that the water is in the shape of a triangular prism with height 6 inches; and the triangular base is a 30-60-90 right triangle with long leg of length 6 inches.

Then do the arithmetic, knowing that the volume of the prism is the area of the base, multiplied by the height.

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular prism with a 6"x6" square base is tilted leftward at a 30o
angle, It contains water just up to the bottom right corner. How many cubic
inches of water does it contain? 
Here is a picture of the front of the tilted rectangular prism. The
horizontal line is the level of the water.



The number of cubic inches of water is the area of the right triangle times
the 6 inches from the front surface of the container to the back surface.

As the other tutor said, it is a 30-60-90 right triangle. 
So the 3 sides are in the ratio 1:√3:2, shortest to longest.
The longer leg is given as 6", so we can find the shorter leg x by the
proportion:

matrix%281%2C2%2Cshorter%2Cleg%29%2Fmatrix%281%2C2%2Clonger%2Cleg%29%22%22=%22%22x%2F6%22%22=%22%221%2Fsqrt%283%29
           x%22%22=%22%226%2Fsqrt%283%29
           x%22%22=%22%22expr%286%2Fsqrt%283%29%29%2Aexpr%28sqrt%283%29%2Fsqrt%283%29%29%22%22=%22%226sqrt%283%29%2F3%22%22=%22%222sqrt%283%29

The area of the triangle is 1/2 times the product of the longer and shorter
legs.  That's 

expr%281%2F2%29%2A6%2A2sqrt%283%29%22%22=%22%226sqrt%283%29 square inches.

We multiply that by the distance from front surface to back surface, which
is 6 inches, and the final answer is

6sqrt%283%29%2A6%22%22=%22%2236sqrt%283%29 cubic inches or about 62.35 cubic inches of water.

Edwin