Archive for the ‘Geometry’ Category

The Triple Pyramid

Sunday, May 28th, 2017

A man named Chadwick wanted to build a square pyramid with three levels to house his wife and kids.

Chadwick wanted the ground floor to be 2000 square feet larger in area than the first floor, which would have 2000 square feet more than the second floor, where he figured to do some meditation and store a good deal of food for his wife Mabel.

Chadwick decided that the length of a slanting edge of the pyramid should be 1.5 times the height of the pyramid.

Can you work out the respective lengths of the side of each floor?

What do you figure is the height of the pyramid?

The Cube Towers

Saturday, August 27th, 2016

An eccentric billionaire decided to build two tall pointed towers consisting of a series of stacked cubes. They would serve decorative purposes being placed in parallel at a large futuristic gate in his theme park. The material to be used would be a high-strength, transparent nanomaterial. The billionaire stated that rainwater and some kind of energy would be collected for undisclosed purposes.

The first cube was to have a side length of 1 cm, the subsequent cube sides 1 cm greater than the previous, up to the last cube with a side length of 100 cm.

The architect scratched his head thinking how to add up the volumes. Can you help him greatly simplify the calculations?

What would be the height of the towers, and their combined volume?