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.

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

F'arc'tion

Age 14 to 16 Short Challenge Level

At the corner of a cube, circular arcs are drawn as shown.

What fraction of the surface area of the cube is shaded?