Question

The fan below has been stretched open as far as it will go to form a semi-circle.

Each of the eighteen sectors formed by the fan consists of the same amount of fabric. The length of
each wooden rod that connects the center of the fan to its edge is 12 cm. The wooden rods are
glued to the fabric forming the fan. Determine the approximate area of each sector.

Answer 1

Area of each sector=
`12.6cm^2`

Explanation:

We are given that

Length of each wooden od that connects the center of the fan to its edge ,r=12 cm

Total number of sectors=18

We have to find the approximate area of each sector.

Area of semi-circle=
`(1)/(2)\pi r^2`

Using the formula

Area of fan=
`(1)/(2)\pi (12)^2=72 \pi cm^2`

Area of each sector=
`(area\;of\;fan)/(Total\;number\;of\;sectors)`

Area of each sector=
`(72\pi)/(18)=(72* 3.14)/(18) cm^2`

Where
`\pi=3.14`

Area of each sector=
`12.56cm^2\approx 12.6 cm^2`