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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?

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Farhan's Poor Square

From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.

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Parallel Parking

Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.

Get Cross

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

White cross on a red circle.

A white cross is placed in a red disc as shown and the resulting figure is symmetrical.
What is the area of the disc still showing?