Home » Puzzles » 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:


Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!


  1. nidhi says:

    i think is the best website to make our maths strong.

  2. CoursesWeb says:

    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:
    Hope it is useful.

  3. Nandeesh says:

    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.

  4. prashant says:

    48 times

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Who is behind QuickerMaths?

I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths

I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more

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