Mirror Mirror Hologram

Calculus Level 5

The image above is of a hologram.

In the GIF, the Black ball is the real object and the Green ball is the virtual image produced.

The Black lines represents the hologram itself and is coated on the inside with a Chrome layer, such that inside the hologram acts like a mirror. (As shown in the GIF)

The Red lines represents the maximum the light can go.

The Red lines indicate that there are some parts of the object where the virtual image does not show:

So now, here's the question:

Dr Boh wants to get a hologram that has a height of \(5\), and also wants to find the volume of the hologram that he would be getting. Given that the volume of that hologram is \(A\), find \[\left\lfloor 100A \right\rfloor \]

Details and Assumptions:

  • The height of the holograph is defined as:



  • You might want to take a look at Brusspup's video first to get an idea of how a hologram works


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