Bantuiin please.... Daruraat

Mapel : Matematika
Materi : Lingkarang - Sudut, Juring dan Busur

Soal No. 3
Garis POR adalah Diameter Lingkaran, maka

∠QOR = 180° - ∠POQ
∠QOR = 180° - 72°
∠QOR = 108°

a. Panjang Busur QR

[tex] \frac{Panjang\ Busur\ QR}{Panjang\ Busur\ PQ} = \frac{\angle QOR}{\angle POQ}\\ \\ \frac{Panjang\ Busur\ QR}{35}=\frac{108}{72} \\ \\ Panjang\ Busur\ QR= 35\times \frac{3}{2}\\ \\\boxed{\bold{Panjang\ Busur\ QR= 52,5\ cm}} [/tex]

b. Keliling Lingkaran

[tex]Keliling=2\times(PQ + QR)\\Keliling=2\times(35+52,5)\\Keliling=2\times87,5\\ \\ \boxed{\bold{Keliling=175\ cm}}[/tex]

Soal No. 4
[tex]\bold{a)\ Juring}\\\\ \alpha =72^o\\r=42cm\\\\Keliling=Panjang\ Busur+(2\times Jari-Jari)\\\\Keliling=(\frac{\alpha}{360^o}\times2 \pi r)+2r\\\\Keliling= (\frac{72^o}{360^o}\times2\times \frac{22}{7}\times42) +(2\times42)\\\\Keliling= (\frac{1}{5}\times2\times22\times6) +(84)\\\\Keliling= (\frac{1}{5}\times264) +(84)\\\\Keliling= (52,8) +(84)\\\\\boxed{\bold{Keliling= 136,8\ cm}}[/tex]

[tex]Luas= \frac{\alpha}{360^o}\times \pi r^2\\\\Luas= \frac{72^o}{360^o}\times \frac{22}{7}\times42\times42\\\\Luas= \frac{1}{5}\times22\times6\times42\\\\Luas= \frac{1}{5}\times22\times6\times42\\\\Luas= \frac{1}{5}\times5.544 \\ \\\boxed{\bold{Luas=1.108,8\ cm^2}}[/tex]

[tex]\bold{b)\ Seperempat\ Cincin}\\\\Keliling\ \frac{1}{4}\ Lingkaran\ Besar:\\\\K_1=\frac{1}{4}\times2\times \pi r\\\\K_1=\frac{1}{4}\times2\times(3,14)\times18\\\\K_1=9\times (3,14)\\\\K_1=28,26\ cm\\\\\\Keliling\ \frac{1}{4}\ Lingkaran\ Kecil:\\\\K_2=\frac{1}{4}\times2\times \pi r\\\\K_2=\frac{1}{4}\times2\times(3,14)\times12\\\\K_2=6\times (3,14)\\\\K_2=18,84\ cm\\\\\\Keliling=K_1+K_2+2(r_1-r_2)\\\\Keliling=28,26+18,84+2(18-12)\\\\Keliling=47,1+2(6)\\\\Keliling=47,1+12 \\\\\boxed{\bold{Keliling=59,1\ cm}}[/tex]

[tex]Luas\ Cincin=Luas\ \frac{1}{4}\ Lingkaran\ Besar -Luas\ \frac{1}{4}\ Lingkaran\ Kecil\\\\Luas\ Cincin= \pi (r_1)^2-\pi (r_2)^2\\ \\Luas\ Cincin= \pi ((r_1)^2-(r_2)^2)\\ \\Luas\ Cincin= (3,14)\times (18^2-12^2)\\ \\Luas\ Cincin= (3,14)\times (324-144)\\ \\Luas\ Cincin= (3,14)\times(180)\\ \\\boxed{\bold{Luas\ Cincin= 565,2\ cm^2}}[/tex]

***Semoga Terbantu***