Maths item of the month
In the diagram various regular polygons, P, have been drawn whose sides are tangents to a circle, C.
Show that for any regular polygon drawn in this way:
Cones from a circle
An angle θ is cut out of a circle of card to create two sectors: a major sector and a minor sector. The two sectors are then folded to make cones.
What angle θ is required to obtain the largest value for the sum of the volumes of the two cones?
An unexpected answer
Mr Teacher sets his class the following problem:
A committee of 3 students is to be chosen from a group of 13 students of which 8 are girls and 5 are boys. The students are selected at random, without replacement. What is the expected number of girls on the committee?
Anne Student immediately responds that the answer is .
She gives the reason that there are 3 students to be chosen and the proportion of girls is so she calculated .
Is she correct?
If proportion of male and female students was different would her method work?