Question

Find the area of the sector of a circle whose diameter is 84 cm and the angle at the centre is 135 degree

Answer 1

• The area of the sector is 2079 cm sq.

Given:

The diameter of the circle is 84 cm

The angle of the sector in the circle is (Ф) = 135°

To find:

The area of the sector

Now,

Radius = diameter/2

Radius (r) = 84/2 = 42 cm

The formula to find the area of the sector when radius and angle (Ф) are given:-

Area of sector = Ф/360 * πr² unit sq.

= 135/360 * 22/7 * 42 * 42

= 135/360 * 22 * 6 * 42

= 135/60 * 22 * 42

= 135/10 * 22 * 7

= 20790/10

= 2079 cm sq.

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If the angle (Ф) of the sector is given and radius of the circle is given and the question asks about the length of the arc of the sector (l)

• Arc length (l) = Ф/360 * 2πr units

Answer 2

GIVEN :-

• Tʜᴇ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴄɪʀᴄʟᴇ ɪs "84ᴄᴍ" .

• Aɴɢʟᴇ sᴜʙᴛᴇɴᴅs ᴀᴛ ᴛʜᴇ ᴄᴇɴᴛʀᴇ ɪs "135°" .

TO FIND :-

• Tʜᴇ ᴀʀᴇᴀ ᴏғ ᴛʜᴇ sᴇᴄᴛᴏʀ .

SOLUTION :-

Wᴇ ʜᴀᴠᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

$\huge\green\star$ Aʀᴇᴀ ᴏғ ᴛʜᴇ sᴇᴄᴛᴏʀ = $\bf\red{\dfrac{\theta}{360}\times{\pi\:r^2}\:}$

• Radius = $\bf{\dfrac{Diameter}{2}}$ = 84/2 = 42cm

• $\bf\red{\theta}$ = 135°

$\purple\checkmark\:\bf{Area\:of\:the\:sector\:=\:\dfrac{135}{360}\times{\dfrac{22}{7}}\times{(42)^2}\:}$

➳ $\rm{Area\:=\:\dfrac{135}{360}\times{\dfrac{22}{\cancel{7}}}\times{\cancel{42}}\times{42}\:}$

➳ $\rm{Area\:=\:\dfrac{135}{\cancel{360}}\times{22}\times{\cancel{6}}\times{42}\:}$

➳ $\rm{Area\:=\:\dfrac{\cancel{135}}{\cancel{60}}\times{22}\times{42}\:}$

➳ $\rm{Area\:=\:\dfrac{9}{\cancel{4}}\times{\cancel{22}}\times{42}\:}$

➳ $\rm{Area\:=\:\dfrac{9}{\cancel{2}}\times{11}\times{\cancel{42}}\:}$

➳ $\rm{Area\:=\:9\times{11}\times{21}\:}$

➳ Aʀᴇᴀ ᴏғ ᴛʜᴇ sᴇᴄᴛᴏʀ = 2079cm²

$\huge\red{\therefore}$ Tʜᴇ ᴀʀᴇᴀ ᴏғ ᴛʜᴇ sᴇᴄᴛᴏʀ ɪs "2079ᴄm²" .