Problems
A cube with a side of 1 m was sawn into cubes with a side of 1 cm and they were in a row (along a straight line). How long was the line?
In some country there are 101 cities, and some of them are connected by roads. However, every two cities are connected by exactly one path.
How many roads are there in this country?
The volume of a pyramid is \(\frac{1}{3}Bh\), where \(B\) is the area of the base and \(h\) is the perpendicular height. What’s the volume of a regular tetrahedron with side length \(1\)?
The Great Pyramid of Giza is the largest pyramid in Egypt. For the purposes of this problem, assume that it’s a perfect square-based pyramid, with perpendicular height \(140\)m and the square has side length \(230\)m.
What is its volume in cubic metres?
A regular octahedron is a solid with eight faces, all of which are equilateral triangles. It can be formed by placing together two square based pyramids at their bases.
What is the volume of an octahedron with side length \(1\)?