Date rewarded: August 14th, 2001.

'

*Excuse me, Slave*', said Princess Vyssa, '

*I have a job for you*'. '

*What is it?*', Burlak groaned??? Princess Vyssa handed the sculptor a big ball of clay. '

*I would like some decorations for my new palace. I want you to build me lots of little pyramids out of this clay. The base has to measure 8 centimeters by 8 centimeters, and they have to be 6 centimeters high.*.

**do you know?**

Prize

Unknown

Unknown

__Click to show/hide solution__

Volume of a pyramid [1]:

V

_{1}= B * h /3 = 8^{2}* 6 / 3 = 128 cm^{3}where B is the area of the base of the pyramid, h is the height of the pyramid.

Volume of the sphere [2]:

V

_{2}= 4/3 * pi * r^{3}= 4/3 * pi * 10^{3}= 4000/3 * pi cm^{3}where r is the radius of the sphere.

Total number of pyramids that Burlak can make:

N = V

_{2}/ V_{1}~ 32.72Therefore, he can make 32 pyramids from the clay sphere.

References:

[1] Pyramid volume

[2] Sphere volume

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