1 out of 3
How efficiently can you pack together disks?
2 out of 3
Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.
2 out of 3
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
2 out of 3
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
2 out of 3
Four quadrants are drawn centred at the vertices of a square . Find the area of the central region bounded by the four arcs.
3 out of 3
3 out of 3
Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap?
3 out of 3
Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.
3 out of 3
Can you find a relationship between the area of the crescents and the area of the triangle?
3 out of 3
Weekly Problem 13 - 2006
If three runners run at the same constant speed around the race tracks, in which order do they finish?
