### Qqq..cubed

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of another cube is 8cms. What is the side length of this cube? Another cube has an edge length of 12cm. At each vertex a tetrahedron with three mutually perpendicular edges of length 4cm is sliced away. What is the surface area and volume of the remaining solid?

### When the Angles of a Triangle Don't Add up to 180 Degrees

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.

### The Spider and the Fly

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

# Changing Areas, Changing Volumes

##### Stage: 4 Challenge Level:
Try working on Changing Areas, Changing Perimeters first, as it is a two-dimensional version of this three-dimensional problem.

If I know two rectangles have the same area, how can I decide, just by looking at their dimensions, which has the greater perimeter?
If I know two cuboids have the same volume, how can I decide, just by looking at their dimensions, which has the greater surface area?