Pyramids

[jason]

The base of the pyramid is 100 x 100 blocks; each successive layer is one less block wide and deep, until the top layer which is only 1 block. Each block is 97 cm wide by 97 cm deep by 63 cm tall.
If one liter of paint can coat exactly three square meters, how many liters are required to coat the entire exposed surface of the pyramid?
Round up to the nearest liter.

[Guest]

The exposed bits of the tops of the blocks need painted
and the exposed vertical faces of the blocks need painted

The tops are all within the area of the base so just same as painting the area of the base

There is 1 block on the top row so it will need 4 vertical faces painted

Next row down will have 2 x 2 blocks so needs 8 vertical faces painted .....and so on until base 100 x 100 needs 400 faces painted....so total faces is sum of the numbers 1 to 100....multiply by 4 = 20200 faces.
Each face is 0.97 x 0.63 so total area = 12344 sq m.
Area of tops = 100 x 0.97 x 100 x 0.97 = 9409 sq m.

Total area = 21753 sq m.

Total litres = 21753 / 3 = 7251 litres of paint.

[Guest]

Did you know that is a 0.333 mm thick coat of paint.