Question

Find the perimeter and area of a sector of a circle of
radius 5cm and its angle is 96º.
​

Answer 1

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ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏꜰ ᴛʜᴇ ꜱᴇᴄᴛᴏʀ ɪꜱ ᴛʜᴇ ꜱᴜᴍ ᴏꜰ ᴛʜᴇ ʟᴇɴɢᴛʜꜱ ᴏꜰ ᴀʟʟ ɪᴛꜱ ʙᴏᴜɴᴅᴀʀɪᴇꜱ. ᴛʜᴜꜱ ᴛʜᴇ ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏꜰ ᴛʜᴇ ꜱᴇᴄᴛᴏʀ ɪꜱ ʟ+2ʀ ᴜɴɪᴛꜱ ᴡʜᴇʀᴇ ʟ ɪꜱ ᴛʜᴇ ᴄɪʀᴄᴜᴍꜰᴇʀᴇɴᴄᴇ ᴏꜰ ꜱᴇᴄᴛᴏʀ ᴀɴᴅ ʀ ɪꜱ ᴛʜᴇ ʀᴀᴅɪᴜꜱ.

$ᴄɪʀᴄᴜᴍꜰᴇʀᴇɴᴄᴇ \: ᴏꜰ \: ᴀ \: ꜱᴇᴄᴛᴏʀ \: ᴏꜰ \: ᴀ \: ᴄɪʀᴄʟᴇ \\ = 2 \: ∗ \: \pi \: ∗ \: r \: ∗ \: \frac{ \alpha }{360}$

$ᴄɪʀᴄᴜᴍꜰᴇʀᴇɴᴄᴇ \: = 2 ∗ \: \pi \: ∗ \: 5 ∗ \: \frac{96}{360} = 8.381$

ᴀꜱ ʀᴀᴅɪᴜꜱ ɪꜱ 5 ᴄᴍ, ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏꜰ ᴛʜᴀᴛ ꜱᴇᴄᴛᴏʀ ɪꜱ 8.381+5+5 = 18.381 ᴄᴍ

$ᴀʀᴇᴀ \: ᴏꜰ \: ꜱᴇᴄᴛᴏʀ \: ᴏꜰ \: ᴀ \: ᴄɪʀᴄʟᴇ = \pi \: ∗ \: {r}^{2} \: ∗ \: \frac{ \alpha }{360}$

$\: ᴀʀᴇᴀ = \pi \: ∗ \: {5}^{2} \: ∗ \: \frac{96}{360} \\ \: \: \: \: \: \: \: \: \: \: \: = 20.9524 {cm}^{2}$

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