Problems

When Gulliver came to Lilliput, he found that there all things were exactly 12 times shorter than in his homeland. Can you say how many Lilliputian matchboxes fit into one of Gulliver’s matchboxes?

Will the entire population of the Earth, all buildings and structures on it, fit into a cube with a side length of 3 kilometres?

When Gulliver came to Lilliput, he found that everything was exactly 12 times shorter than in his homeland. Can you say how many Lilliputian matchboxes fit into the matchbox of Gulliver?

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?

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 \(1\)?