Round 21

Date released: August 10th, 2001.
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..

Burlak looked at the ball of clay, and measured it. It's diameter was 20 centimeters, and it seemed to be a perfect sphere. He wondered how many pyramids he could make... do you know?

Prize
Unknown

Click to show/hide solution

Volume of a pyramid [1]:

V₁ = B * h /3 = 8² * 6 / 3 = 128 cm³

where B is the area of the base of the pyramid, h is the height of the pyramid.

Volume of the sphere [2]:

V₂ = 4/3 * pi * r³ = 4/3 * pi * 10³ = 4000/3 * pi cm³

where r is the radius of the sphere.

Total number of pyramids that Burlak can make:

N = V₂ / V₁ ~ 32.72

Therefore, he can make 32 pyramids from the clay sphere.

References:
[1] Pyramid volume
[2] Sphere volume