Jawaban:
No. 3
a. Diketahui : L = 154cm²
Cara :
[tex]luas = \pi \times {r}^{2} \\ 154 = \frac{22}{7} \times {r}^{2} \\ {r}^{2} = \frac{154}{ \frac{22}{7} } \\ {r}^{2} = 154 \times \frac{7}{22} \\ {r}^{2} = 7 \times 7 \\ {r}^{2} = 49 \\ r = \sqrt{49} \\ r (jari - jari)= 7cm \\ \\ diameter = 2 \times r = 2 \times 7 = 14cm[/tex]
b. Diketahui : L = 314cm² , phi = 3,14
[tex]luas = \pi \times {r}^{2} \\ 314 = 3.14 \times {r}^{2} \\ {r}^{2} = \frac{314}{3.14} \\ {r}^{2} = 100 \\ r = \sqrt{100} \\ r(jari - jari) = 10 \\ diameter = 2 \times r = 2 \times 10 = 20[/tex]
c. Diketahui : L = 616cm²
[tex]luas = \pi \times {r}^{2} \\ 616 = \frac{22}{7} \times {r}^{2} \\ {r}^{2} = \frac{616}{ \frac{22}{7} } \\ {r}^{2} = 616 \times \frac{7}{22} \\ {r}^{2} = 28 \times 7 \\ {r}^{2} = 196 \\ r = \sqrt{196} \\ r(jari - jari) = 14cm \\ diameter = 2 \times r = 2 \times 14 = 28cm[/tex]
d. Diketahui : L = 1256cm² , phi = 3,14
[tex]luas = \pi \times {r}^{2} \\ 1256 = 3.14 \times {r}^{2} \\ {r}^{2} = \frac{1256}{ 3.14} \\ {r}^{2} = 400 \\ r = \sqrt{400}\\ r = 20cm \\ diameter = 2 \times r = 2 \times 20 = 40cm[/tex]
e. Diketahui : L = 1386cm²
[tex]luas = \pi \times {r}^{2} \\ 1386 = \frac{22}{7} \times {r}^{2} \\ {r}^{2} = \frac{1386}{ \frac{22}{7} } \\ {r}^{2} = 1386 \times \frac{7}{22} \\ {r}^{2} = 63 \times 7 \\ {r}^{2} = 441 \\ r = \sqrt{441} \\ r(jari - jari) = 21cm \\ diameter = 2 \times r = 2 \times 14 = 42cm[/tex]
f. Diketahui : L = 3850cm²
[tex]luas = \pi \times {r}^{2} \\ 3850 = \frac{22}{7} \times {r}^{2} \\ {r}^{2} = \frac{3850}{ \frac{22}{7} } \\ {r}^{2} = 3850 \times \frac{7}{22} \\ {r}^{2} = 175 \times 7 \\ {r}^{2} = 1225 \\ r = \sqrt{1225} \\ r(jari - jari) = 35cm \\ diameter = 2 \times r = 2 \times 35 = 70cm[/tex]
No. 4
a. Diketahui : r = 7cm
daerah yang di warnai = 1/2 lingkaran
[tex]luas = \frac{1}{2} \times \pi \times {r}^{2} \\ luas = \frac{1}{2} \times \frac{22}{7} \times {7}^{2} \\ luas = \frac{1}{2} \times 22 \times 7 \\ luas = 11 \times 7 \\ luas = 77 {cm}^{2} [/tex]
b. Diketahui : d = 20cm -> r = 10
Daerah yang di arsir = 1/2 lingkaran
[tex]luas = \frac{1}{2} \times \pi \times {r}^{2} \\ luas = \frac{1}{2} \times 3.14 \times {10}^{2} \\ luas = \frac{1}{2} \times 3.14 \times 100 \\ luas = 3,14 \times 50 \\ luas = 157 {cm}^{2} [/tex]
c. Diketahui : r = 21
Luas daerah yang di arsir = 3/2 lingkaran
[tex]luas = \frac{3}{2} \times \pi \times {r}^{2} \\ luas = \frac{3}{2} \times \frac{22}{7} \times {21}^{2} \\ luas = \frac{3}{2} \times 22 \times 21 \times 3 \\ luas = 3 \times 11 \times 21 \times 3 \\ luas = 2079{cm}^{2} [/tex]
No. 5
a. Diketahui : Panjang = Diameter = 28cm
Lebar = 24cm
[tex]luas total = (luaspersegi) + (luas1/2lingkaran)\\ luas total = (p \times l) + (\frac{1}{2} \times \pi \times {r}^{2}) \\ luas total = (28 \times 24) + (\frac{1}{2} \times \frac{22}{7} \times 14 \times 14) \\ luas total = 675 + (11 \times 14 \times 2) \\ luas total = 675 + 308 \\\ = 983cm²[/tex]
b. Diketahui : Panjang = Diameter = Alas = 42cm , Lebar = Tinggi = 18cm
[tex]luas total = (luassegitiga) + (luas1/2lingkaran)\\ luas total = (\frac{1}{2} \times a \times b) + (\frac{1}{2} \times \pi \times {r}^{2}) \\ luas total = (\frac{1}{2} \times 42 \times 18) + (\frac{1}{2} \times \frac{22}{7} \times 21 \times 21) \\ luas total = (21 \times 18) + (11 \times 21 \times 3) \\ luas total = 378 + 396 \\ = 774cm²[/tex]
c. Diketahui : Sisi = jari-jari = 35cm , 1/4lingkaran
[tex]luas total = (luaspersegi) + (luas1/4lingkaran)\\ luas total = (s \times s) + (\frac{1}{4} \times \pi \times {r}^{2}) \\ luas total = (35 \times 35) + (\frac{1}{4} \times \frac{22}{7} \times 35 \times 35) \\ luas total = 1225 + (\frac{11 \times 5 \times 35}{2}) \\ luas total = 1225 + (\frac{1925}{2}) \\ = 1225 + 926,5 \\ = 2151,5cm²[/tex]
d. Maaf banget buat yang D aku ngga tau
e. Diketahui : diameter lingkaran kecil = 28cm , diameter lingkaran besar 56cm
[tex]luas total = (luaslingkaranbesar) - (luaslingkarankecil)\\ luas total = (\pi \times {r}^{2}) - (\pi \times {r}^{2}) \\ luas total = (\frac{22}{7} \times 28 \times 28) - (\frac{22}{7} \times 14 \times 14) \\ luas total = (22 \times 4 \times 28) - (22 \times 2 \times 14) \\ = 2464 - 616 \\ = 1848cm²[/tex]
f. Diketahui : Diameter 1/2 lingkaran besar = 84cm , diameter 1/2 lingkaran kecil = 28cm
Cara:
[tex]luas total = (luas1/2lingkaranbesar) - (luas1/2lingkarankecil)\\ luas total = (\frac{1}{2} \times \pi \times {r}^{2}) - (\frac{1}{2} \times \pi \times {r}^{2}) \\ luas total = (\frac{1}{2} \times \frac{22}{7} \times 42 \times 42) - (\frac{22}{7} \times 14 \times 14) \\ luas total = (11 \times 6 \times 42) - (11 \times 2 \times 14) \\ = 2772 - 308 \\ = 2464cm²[/tex]
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Jawaban:
No. 3
a. Diketahui : L = 154cm²
Cara :
[tex]luas = \pi \times {r}^{2} \\ 154 = \frac{22}{7} \times {r}^{2} \\ {r}^{2} = \frac{154}{ \frac{22}{7} } \\ {r}^{2} = 154 \times \frac{7}{22} \\ {r}^{2} = 7 \times 7 \\ {r}^{2} = 49 \\ r = \sqrt{49} \\ r (jari - jari)= 7cm \\ \\ diameter = 2 \times r = 2 \times 7 = 14cm[/tex]
b. Diketahui : L = 314cm² , phi = 3,14
Cara :
[tex]luas = \pi \times {r}^{2} \\ 314 = 3.14 \times {r}^{2} \\ {r}^{2} = \frac{314}{3.14} \\ {r}^{2} = 100 \\ r = \sqrt{100} \\ r(jari - jari) = 10 \\ diameter = 2 \times r = 2 \times 10 = 20[/tex]
c. Diketahui : L = 616cm²
Cara :
[tex]luas = \pi \times {r}^{2} \\ 616 = \frac{22}{7} \times {r}^{2} \\ {r}^{2} = \frac{616}{ \frac{22}{7} } \\ {r}^{2} = 616 \times \frac{7}{22} \\ {r}^{2} = 28 \times 7 \\ {r}^{2} = 196 \\ r = \sqrt{196} \\ r(jari - jari) = 14cm \\ diameter = 2 \times r = 2 \times 14 = 28cm[/tex]
d. Diketahui : L = 1256cm² , phi = 3,14
Cara :
[tex]luas = \pi \times {r}^{2} \\ 1256 = 3.14 \times {r}^{2} \\ {r}^{2} = \frac{1256}{ 3.14} \\ {r}^{2} = 400 \\ r = \sqrt{400}\\ r = 20cm \\ diameter = 2 \times r = 2 \times 20 = 40cm[/tex]
e. Diketahui : L = 1386cm²
Cara :
[tex]luas = \pi \times {r}^{2} \\ 1386 = \frac{22}{7} \times {r}^{2} \\ {r}^{2} = \frac{1386}{ \frac{22}{7} } \\ {r}^{2} = 1386 \times \frac{7}{22} \\ {r}^{2} = 63 \times 7 \\ {r}^{2} = 441 \\ r = \sqrt{441} \\ r(jari - jari) = 21cm \\ diameter = 2 \times r = 2 \times 14 = 42cm[/tex]
f. Diketahui : L = 3850cm²
Cara :
[tex]luas = \pi \times {r}^{2} \\ 3850 = \frac{22}{7} \times {r}^{2} \\ {r}^{2} = \frac{3850}{ \frac{22}{7} } \\ {r}^{2} = 3850 \times \frac{7}{22} \\ {r}^{2} = 175 \times 7 \\ {r}^{2} = 1225 \\ r = \sqrt{1225} \\ r(jari - jari) = 35cm \\ diameter = 2 \times r = 2 \times 35 = 70cm[/tex]
No. 4
a. Diketahui : r = 7cm
Cara :
daerah yang di warnai = 1/2 lingkaran
[tex]luas = \frac{1}{2} \times \pi \times {r}^{2} \\ luas = \frac{1}{2} \times \frac{22}{7} \times {7}^{2} \\ luas = \frac{1}{2} \times 22 \times 7 \\ luas = 11 \times 7 \\ luas = 77 {cm}^{2} [/tex]
b. Diketahui : d = 20cm -> r = 10
Cara :
Daerah yang di arsir = 1/2 lingkaran
[tex]luas = \frac{1}{2} \times \pi \times {r}^{2} \\ luas = \frac{1}{2} \times 3.14 \times {10}^{2} \\ luas = \frac{1}{2} \times 3.14 \times 100 \\ luas = 3,14 \times 50 \\ luas = 157 {cm}^{2} [/tex]
c. Diketahui : r = 21
Cara :
Luas daerah yang di arsir = 3/2 lingkaran
[tex]luas = \frac{3}{2} \times \pi \times {r}^{2} \\ luas = \frac{3}{2} \times \frac{22}{7} \times {21}^{2} \\ luas = \frac{3}{2} \times 22 \times 21 \times 3 \\ luas = 3 \times 11 \times 21 \times 3 \\ luas = 2079{cm}^{2} [/tex]
No. 5
a. Diketahui : Panjang = Diameter = 28cm
Lebar = 24cm
Cara :
[tex]luas total = (luaspersegi) + (luas1/2lingkaran)\\ luas total = (p \times l) + (\frac{1}{2} \times \pi \times {r}^{2}) \\ luas total = (28 \times 24) + (\frac{1}{2} \times \frac{22}{7} \times 14 \times 14) \\ luas total = 675 + (11 \times 14 \times 2) \\ luas total = 675 + 308 \\\ = 983cm²[/tex]
b. Diketahui : Panjang = Diameter = Alas = 42cm , Lebar = Tinggi = 18cm
Cara :
[tex]luas total = (luassegitiga) + (luas1/2lingkaran)\\ luas total = (\frac{1}{2} \times a \times b) + (\frac{1}{2} \times \pi \times {r}^{2}) \\ luas total = (\frac{1}{2} \times 42 \times 18) + (\frac{1}{2} \times \frac{22}{7} \times 21 \times 21) \\ luas total = (21 \times 18) + (11 \times 21 \times 3) \\ luas total = 378 + 396 \\ = 774cm²[/tex]
c. Diketahui : Sisi = jari-jari = 35cm , 1/4lingkaran
Cara :
[tex]luas total = (luaspersegi) + (luas1/4lingkaran)\\ luas total = (s \times s) + (\frac{1}{4} \times \pi \times {r}^{2}) \\ luas total = (35 \times 35) + (\frac{1}{4} \times \frac{22}{7} \times 35 \times 35) \\ luas total = 1225 + (\frac{11 \times 5 \times 35}{2}) \\ luas total = 1225 + (\frac{1925}{2}) \\ = 1225 + 926,5 \\ = 2151,5cm²[/tex]
d. Maaf banget buat yang D aku ngga tau
e. Diketahui : diameter lingkaran kecil = 28cm , diameter lingkaran besar 56cm
Cara :
[tex]luas total = (luaslingkaranbesar) - (luaslingkarankecil)\\ luas total = (\pi \times {r}^{2}) - (\pi \times {r}^{2}) \\ luas total = (\frac{22}{7} \times 28 \times 28) - (\frac{22}{7} \times 14 \times 14) \\ luas total = (22 \times 4 \times 28) - (22 \times 2 \times 14) \\ = 2464 - 616 \\ = 1848cm²[/tex]
f. Diketahui : Diameter 1/2 lingkaran besar = 84cm , diameter 1/2 lingkaran kecil = 28cm
Cara:
[tex]luas total = (luas1/2lingkaranbesar) - (luas1/2lingkarankecil)\\ luas total = (\frac{1}{2} \times \pi \times {r}^{2}) - (\frac{1}{2} \times \pi \times {r}^{2}) \\ luas total = (\frac{1}{2} \times \frac{22}{7} \times 42 \times 42) - (\frac{22}{7} \times 14 \times 14) \\ luas total = (11 \times 6 \times 42) - (11 \times 2 \times 14) \\ = 2772 - 308 \\ = 2464cm²[/tex]
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