Area - circles, sectors and segments

problem

Handy Angles

Age

11 to 14

Challenge level

Weekly Problem 39 - 2008
How big is the angle between the hour hand and the minute hand of a clock at twenty to five?
problem

Two Circles

Age

14 to 16

Challenge level

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?
problem

Square Pegs

Age

11 to 14

Challenge level

Which is a better fit, a square peg in a round hole or a round peg in a square hole?
problem

Running Race

Age

14 to 16

Challenge level

Weekly Problem 13 - 2006
If three runners run at the same constant speed around the race tracks, in which order do they finish?
problem

Eyelids

Age

14 to 16

Challenge level

Can you work out the shaded area surrounded by these arcs?
problem

Circular Area

Age

7 to 11

Challenge level

How could you find out the area of a circle? Take a look at these ways.
problem

Efficient Packing

Age

14 to 16

Challenge level

How efficiently can you pack together disks?
problem

F'arc'tion

Age

14 to 16

Challenge level

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.
problem

Giant Holly Leaf

Age

14 to 16

Challenge level

Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).
problem

The Pillar of Chios

Age

14 to 16

Challenge level

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.