# Relationship between Length, Area and Volume

Lot of time we face problems related to change in area or volume when some dimension of the 2-dimensional figures or 3-dimensional object changes.

Here I am giving a small mathematical problem, which can be solved as soon as you finish reading it if you know the simple trick to answer it. In my next post I will explain this very helpful trick of finding the change in area of 2-dimensionals figures and volume of 3-dimesionals figures if their dimensions changes. Also relationships between surface area and volume of cube, sphere, pyramid, etc. will be explained. These tricks come very handy in competitive examinations.

**Geometric Puzzle**

I have a miniature Pyramid of Egypt. It is 6 inches in height. I was invited to display it at an exhibition. I felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is 1/8 times the density of the material used for the miniature. I did some calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid?

Now it’s upto you to answer this and figure what could be the trick to solve such questions.

**Leave your answers and comments below:**

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Hi,

Using the math formulas , I made a script with JavaScript that calculate the volume and surface area of various 3D objects (cube, barrel, prism, sphere, etc.). I post it on the page:

http://www.coursesweb.net/javascript/volume-surface-area-calculator-3d-objects_s2

Hope it is useful.

The density is 1/8th.

The volume of scaled up pyramid cane be 8 times for the same final weight.

8 = 2^3.

So doubling the dimensions results in 8 times the volume.

It means the height of the new pyramid is 2 times.

48 times