Hitunglah luas permukaan dan volume model bangun ruang berikut!

<p>Jawab:&nbsp;</p><p>Volume bangun ruang adalah 20 kubus satuan.</p><p>luas permukaan bangun ruang adalah 62 satuan persegi.</p><p>Pembahasan:</p><p><strong>Menentukan volume bangun ruang.</strong></p><p>Balok 1 memiliki panjang 3 satuan, lebar 4 satuan dan tinggi 1 satuan.</p><p>Volume balok 1 = 3×4×1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 12</p><p>Sehingga, volume balok 1 adalah 12 kubus satuan.</p><p>Balok 2 memiliki panjang 2 satuan, lebar 3 satuan dan tinggi 1 satuan.</p><p>Volume balok 2 = 2×3×1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 6</p><p>Sehingga, volume balok 2 adalah 6 kubus satuan.</p><p>Balok 3 memiliki panjang 1 satuan, lebar 2 satuan dan tinggi 1 satuan.</p><p>Volume balok 3 = 1×2×1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 2</p><p>Sehingga, volume balok 3 adalah 2 kubus satuan.</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; = 12+6+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; = 20</p><p>Jadi, volume bangun ruang adalah 20 kubus satuan.</p><p><strong>Menentukan luas permukaan bangun ruang.</strong></p><p>Balok 1 memiliki panjang 3 satuan, lebar 4 satuan dan tinggi 1 satuan.</p><p>Luas permukaan balok = 2((3×4)+(3×1)+(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; &nbsp; = 2(12+3+4)</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; = 2(19)</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; = 38</p><p>Luas permukaan balok 1 adalah 38 satuan persegi.</p><p>Balok 2 memiliki panjang 2 satuan, lebar 3 satuan dan tinggi 1 satuan.</p><p>Luas permukaan balok = 2((2×3)+(2×1)+(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; = 2(6+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; = 2(11)</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; = 22</p><p>Luas permukaan balok 2 adalah 22 satuan persegi.</p><p>Balok 3 memiliki panjang 1 satuan, lebar 2 satuan dan tinggi 1 satuan.</p><p>Luas permukaan balok = 2((1×2)+(1×1)+(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; = 2(2+1+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; = 2(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; = 10</p><p>Luas permukaan balok 3 adalah 10 satuan persegi.</p><p>Terdapat 2 sisi yang saling berimpit.</p><p>Persegi panjang dengan panjang 2 satuan dan lebar 3 satuan.</p><p>Luas persegi panjang berimpit = 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; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 6</p><p>Persegi panjang dengan panjang 1 satuan dan lebar 2 satuan.</p><p>Luas persegi panjang berimpit = 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; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 2</p><p>Luas persegi panjang yang berimpit = 6+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; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 8</p><p>Sehingga, luas persegi panjang yang berimpit adalah 8 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; = 38+22+10-8</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; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 62</p><p>Jadi, luas permukaan bangun ruang di atas adalah 62 satuan persegi.</p><p>&nbsp;</p><p><strong><u>Jadi, jawaban yang benar adalah</u></strong></p><p><strong><u>Volume bangun ruang adalah 20 kubus satuan.</u></strong></p><p><strong><u>luas permukaan bangun ruang adalah 62 satuan persegi.</u></strong></p>