Six identical sectors, each subtending an angle of 60∘ at the centre of a circle of radius 7 cm, are arranged with their straight edges meeting at a common point to form a decorative flower-shaped plate.
Work out the following:
a. Show that the total area of the plate can be expressed as 6×61πr2, where r is the radius of each sector.
b. Calculate the numerical value of the area of the plate, taking π=722.
c. Find the length of the outer boundary of the plate (the petals), giving the answer to one decimal place.