Penjelasan dengan langkah-langkah:
Luas
1.
Luas prisma segitiga
= at∆ + (a + b + c)t - pl
= 6 × 4 + (6 + 5 + 5)12 - 6 × 12
= 6 × 4 + 16 × 12 - 6 × 12
= 144 cm²
Luas balok
= 2(pl + pt + lt) - pl
= 2(6 × 12 + 6 × 10 + 12 × 10) - 6 × 12
= 2(72 + 60 + 120) - 6 × 12
= 2 × 252 - 6 × 12
= 432 cm²
Luas gabungan
= luas prisma segitiga + luas balok
= 144 + 432
= 576 cm²
2.
Luas kerucut
= πr(r + s) - πr²
= 3,14 × 8(8 + 10) - 3,14 × 8²
= 3,14 × 8 × 18 - 3,14 × 8²
= 234,56 cm²
Luas tabung
= 2πr(r + t) - πr²
= 2 × 3,14 × 8(8 + 18) - 3,14 × 8²
= 2 × 3,14 × 8 × 26 - 3,14 × 8²
= 1.088,64 cm²
= luas kerucut + luas tabung
= 234,56 + 1.088,64
= 3.433,2 cm²
3.
Luas ½ bola
= ½4πr² - πr²
= 1/2 × 4 × 22/7 × 7² - 22/7 × 7²
= 154 cm²
= 2 × 22/7 × 7(7 + 9) - 22/7 × 7²
= 2 × 22/7 × 7 × 16 - 22/7 × 7²
= 550 cm²
= luas ½ bola + luas tabung
= 154 + 550
= 704 cm²
4.
= 2 × 3,14 × 6,3(6,3 + 5) - 3,14 × 6,3²
= 2 × 3,14 × 6,3 × 11,3 - 3,14 × 6,3²
= 49,455 cm²
= 10,5 × 4 × 3,14 × 6,3² - 3,14 × 6,3²
= 186,9399 cm²
Volume
Volume prisma segitiga
= (½at∆)t
= (½ × 6 × 4)12
= 12 × 12
= 144 cm³
Volume balok
= plt
= 6 × 10 × 12
= 720 cm³
Volume gabungan
= volume prisma segitiga + volume balok
= 144 + 720
= 864 cm³
Volume kerucut
= ⅓πr²t
= ⅓ × 3,14 × 8² × 6
= 401,92 cm³
Volume tabung
= πr²t
= 3,14 × 8² × 6
= 1.205,76 cm³
= volume kerucut + volume tabung
= 401,92 + 1.205,76
= 1.607,68 cm³
Volume ½ bola
= 1/2 × 4/3πr³
= 1/2 × 4/3 × 22/7 × 7³
= 718,66 cm³
= 22/7 × 7³ × 9
= 1.386 cm³
= volume ½ bola + volume tabung
= 718,66 + 1.386
= 2.104,66 cm³
= ⅓ × 3,14 × 6,3² × 3,9
= 160,3944342 cm³
= 1/2 × 1,33 × 3,14 × 6,3³
= 522,1231407 cm³
= volume kerucut + volume ½ bola
= 160,3944342 + 522,1231407
= 682,5175749 cm³
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Penjelasan dengan langkah-langkah:
Luas
1.
Luas prisma segitiga
= at∆ + (a + b + c)t - pl
= 6 × 4 + (6 + 5 + 5)12 - 6 × 12
= 6 × 4 + 16 × 12 - 6 × 12
= 144 cm²
Luas balok
= 2(pl + pt + lt) - pl
= 2(6 × 12 + 6 × 10 + 12 × 10) - 6 × 12
= 2(72 + 60 + 120) - 6 × 12
= 2 × 252 - 6 × 12
= 432 cm²
Luas gabungan
= luas prisma segitiga + luas balok
= 144 + 432
= 576 cm²
2.
Luas kerucut
= πr(r + s) - πr²
= 3,14 × 8(8 + 10) - 3,14 × 8²
= 3,14 × 8 × 18 - 3,14 × 8²
= 234,56 cm²
Luas tabung
= 2πr(r + t) - πr²
= 2 × 3,14 × 8(8 + 18) - 3,14 × 8²
= 2 × 3,14 × 8 × 26 - 3,14 × 8²
= 1.088,64 cm²
Luas gabungan
= luas kerucut + luas tabung
= 234,56 + 1.088,64
= 3.433,2 cm²
3.
Luas ½ bola
= ½4πr² - πr²
= 1/2 × 4 × 22/7 × 7² - 22/7 × 7²
= 154 cm²
Luas tabung
= 2πr(r + t) - πr²
= 2 × 22/7 × 7(7 + 9) - 22/7 × 7²
= 2 × 22/7 × 7 × 16 - 22/7 × 7²
= 550 cm²
Luas gabungan
= luas ½ bola + luas tabung
= 154 + 550
= 704 cm²
4.
Luas kerucut
= 2πr(r + t) - πr²
= 2 × 3,14 × 6,3(6,3 + 5) - 3,14 × 6,3²
= 2 × 3,14 × 6,3 × 11,3 - 3,14 × 6,3²
= 49,455 cm²
Luas ½ bola
= ½4πr² - πr²
= 10,5 × 4 × 3,14 × 6,3² - 3,14 × 6,3²
= 186,9399 cm²
Volume
1.
Volume prisma segitiga
= (½at∆)t
= (½ × 6 × 4)12
= 12 × 12
= 144 cm³
Volume balok
= plt
= 6 × 10 × 12
= 720 cm³
Volume gabungan
= volume prisma segitiga + volume balok
= 144 + 720
= 864 cm³
2.
Volume kerucut
= ⅓πr²t
= ⅓ × 3,14 × 8² × 6
= 401,92 cm³
Volume tabung
= πr²t
= 3,14 × 8² × 6
= 1.205,76 cm³
Volume gabungan
= volume kerucut + volume tabung
= 401,92 + 1.205,76
= 1.607,68 cm³
3.
Volume ½ bola
= 1/2 × 4/3πr³
= 1/2 × 4/3 × 22/7 × 7³
= 718,66 cm³
Volume tabung
= πr²t
= 22/7 × 7³ × 9
= 1.386 cm³
Volume gabungan
= volume ½ bola + volume tabung
= 718,66 + 1.386
= 2.104,66 cm³
4.
Volume kerucut
= ⅓πr²t
= ⅓ × 3,14 × 6,3² × 3,9
= 160,3944342 cm³
Volume ½ bola
= 1/2 × 4/3πr³
= 1/2 × 1,33 × 3,14 × 6,3³
= 522,1231407 cm³
Volume gabungan
= volume kerucut + volume ½ bola
= 160,3944342 + 522,1231407
= 682,5175749 cm³