Hitunglah luas permukaan dan volume model bangun ruang berikut!

<p>Jawab:&nbsp;</p><p>Volume bangun ruang adalah 14 kubus satuan.</p><p>Luas permukaan bangun ruang adalah 47 satuan persegi.</p><p>Pembahasan:</p><p><strong>Menentukan volume bangun ruang.</strong></p><p>Langkah 1. Menentukan volume balok 1.</p><p>Balok 1 memiliki panjang 3 satuan, lebar 3 satuan dan tinggi 1 satuan.</p><p>Volume balok 1 = 3×3×1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 9</p><p>Langkah 2. menentukan volume balok 2.</p><p>Balok 2 memiliki panjang 2 satuan, lebar 2 satuan dan tinggi 1 satuan.</p><p>Volume balok 2 = 2×2×1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 4</p><p>Langkah 3. Menentukan volume balok 3.&nbsp;</p><p>Balok 3 memiliki panjang 1 satuan, lebar 1 satuan dan tinggi 1 satuan.</p><p>Volume balok 3 = 1×1×1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 1</p><p>&nbsp;</p><p>Volume bangun ruang = vol balok 1 + vol balok 2 + vol balok 3</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 9+4+1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 14</p><p>Jadi, volume bangun ruang adalah 14 kubus satuan.</p><p><strong>Menentukan luas permukaan bangun ruang.</strong></p><p>Balok 1 memiliki panjang 3 satuan, lebar 3 satuan dan tinggi 1 satuan.</p><p>Luas permukaan balok 1 = 2((3×3)+(3×1)+(3×1))</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 2(9+3+3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 2(15)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 30</p><p>Luas permukaan balok 1 adalah 30 satuan persegi.</p><p>Balok 2 memiliki panjang 2 satuan, lebar 2 satuan dan tinggi 1 satuan.</p><p>Luas permukaan balok 2 = 2((2×2)+(2×1)+(2×1))</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 2(4+2+2)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 2(8)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 16</p><p>Luas permukaan balok 2 adalah 16 satuan persegi.</p><p>Balok 3 memiliki panjang 1 satuan, lebar 1 satuan dan tinggi 1 satuan.</p><p>Luas permukaan balok 3 = 2((1×1)+(1×1)+(1×1))</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 2(1+1+1)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 2(3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 6</p><p>Luas permukaan balok 3 adalah 6 satuan persegi.</p><p>Terdapat sisi yang saling berimpit. Luas sisi yang berimpit tersebut adalah</p><p>Persegi dengan panjang 2 satuan dan lebar 2 satuan.</p><p>Luas persegi berimpit = 2×2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 4 satuan persegi.</p><p>Persegi dengan panjang 1 satuan dan lebar 1 satuan.&nbsp;</p><p>Luas persegi berimpit = 2×2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 4 satuan persegi.</p><p>Sehingga, luas persegi yang berimpit adalah 4+1 = 5 satuan persegi.</p><p>Luas permukaan bangun ruang = L_{balok 1}+L_{balok 2}+L_{balok 3}-L_berimpit</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 30+16+6-5</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 47</p><p>Sehingga, luas permukaan bangun ruang di atas adalah 47 satuan persegi.</p><p>&nbsp;</p><p><strong><u>Jadi, jawaban yang benar adalah&nbsp;</u></strong></p><p><strong><u>Volume bangun ruang adalah 14 kubus satuan.</u></strong></p><p><strong><u>Luas permukaan bangun ruang adalah 47 satuan persegi.</u></strong></p><p>&nbsp;</p>