Asked by Niel

A Japanese fan can be made by sliding open its 7 small sections (or leaves), which are each in the form
of sectors of a circle having central angle of 15. If the radius of this fan is 24 cm, find out the length of
the lace that is required to cover its entire boundary. [USE Pi=22/7]
Answered by Reiny
As I understand the question, you simply want the circumference of a sector of central angle 7(15°) or 105° with a radius of 24 cm

circumference of a circle with radius 24 is 48π cm
so using a simple ratio ...
105/360 = x/48π
gives an arc length of 105(48π)/360
which is appr 43.98 cm
add on the two radii would give you a total of
91.98 cm

(must be quite an old text book question if they suggest using 22/7 for π. Just about every modern calculator I have seen has the value of π built in to about 10 decimal places)
Answered by Sakshi chawla
Total angle given =7(15°) &r= 24
Length of lace required = circumference of arc + 2r
angle given/360*2*pi*r +2r
105/360*2*22/7*24=92cm
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