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How can 2 prisms have the same volume but different dimensions?
If you double the cross-sectional area and halve the length, you will still have the same volume but the dimensions will be different.
How does dimensional analysis work in real life?
Basically, if you check the dimensions of an equation and get different dimensions on the left and on the right, the equation is definitely wrong. If you get the same dimensions, it MAY be right.
What 3-D is in relation to the Cartesian coordinate system?
The Cartesian coordinate system can be used in 3 or more dimensions.
If the area is 10 square feet what are the dimensions?
If I only know the area, I can't tell you the dimensions. It all depends on the shape. A circle and a square give two different answers, and there are millions of rectangles, with different dimensions, that are all perfectly good and completely correct answers.
How are the different dimension related to one another?
Space can be divided into n different dimensions. Every dimension is orthogonal to rest all the dimensions. That is the dot product of x with y is zero (y not equal to x).
