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]

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

To find the length of the lace required to cover the entire boundary of the fan, we need to find the circumference of the fan.

The 7 small sections of the fan can be seen as 7 sectors of a circle with a central angle of 15 degrees and a radius of 24 cm.

First, let's find the circumference of one sector of the fan using the formula:

Circumference of sector = (central angle / 360 degrees) * 2 * π * radius

Given:
Central angle = 15 degrees
Radius = 24 cm
π = 22/7

Circumference of one sector = (15/360) * 2 * (22/7) * 24

Simplifying the expression:

Circumference of one sector = (1/24) * 2 * (22/7) * 24
= (22/7) * 2
= 44/7

Since there are 7 small sections, the length of the lace required to cover the entire boundary is:

Length of lace = Circumference of one sector * 7
= (44/7) * 7
= 44 cm

Therefore, the length of the lace required to cover the entire boundary of the fan is 44 cm.

To find the length of the lace required to cover the entire boundary of the Japanese fan, we need to calculate the circumference of each small section or leaf and then sum them up.

Given that each small section is in the form of a sector of a circle with a central angle of 15 degrees and a radius of 24 cm, we can calculate the circumference of each section using the formula:

Circumference = (Angle / 360) * 2 * π * Radius

Let's substitute the given values into the formula:

Angle = 15 degrees
Radius = 24 cm
π = 22/7

Circumference = (15 / 360) * 2 * (22/7) * 24

Now, let's calculate the circumference of each section:

Circumference = (15 / 360) * 2 * (22/7) * 24
Circumference = (1/24) * (2/1) * (22/7) * 24
Circumference = (1/1) * (22/7)
Circumference = 22/7

Now, we know that each section's circumference is 22/7 cm.

Since there are 7 small sections in the fan, to find the total length of the lace needed to cover the entire boundary, we multiply the circumference of one section by the number of sections:

Total length of lace = 7 * (22/7)
Total length of lace = 22 cm * 7
Total length of lace = 154 cm

Therefore, the length of lace required to cover the entire boundary of the Japanese fan is 154 cm.

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)