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Hitunglah volume dari benda tersebut! Pembahasan Volume dari 1/2 bola: Volume dari tabung: Volume dari kerucut: Volume bangun = 19404 + 29106 + 13860 = 62370 cm 3 Soal No. 7 Sebuah benda disusun dari bentuk-bentuk setengah bola, tabung dan kerucut seperti pada gambar berikut! ![]() Tentukan luas permukaan dari benda tersebut! Pembahasan Luas dari 1/2 bola: L 1 = 2πr 2 = 2 x 22/7 x 21 x 21 = 2772 cm 2 Luas dari selimut tabung: L 2 = 2πrt = 2 x 22/7 x 21 x 21 = 2772 cm 2 Luas dari selimut kerucut: Garis pelukis kerucut s = √(21 2 + 28 2) s = 35 cm L 3 = πrs = 22/7 x 21 x 35 = 2310 cm 2 Luas permukaan bangun di atas: L = 2772 + 2772 + 2310 = 7854 cm 2 Soal No. 8 Sebuah tandon air berbentuk tabung dalam keadaan kosong. Jari-jari tandon air adalah 1 m dan tingginya 1,2 m. Jika tandon diisi air dari kran yang memiliki debit 628 liter/menit, maka waktu yang diperlukan tandon hingga terisi penuh adalah. 24 menit Pembahasan Tandon air: r = 1 m = 10 dm t = 1,2 m = 12 dm Volume tandon dalam liter: V = πr 2 t = 3,14 x 10 x 10 x 12 = 3768 dm 3 = 3768 liter Waktu yang diperlukan untuk tandon penuh dari kondisi kosong: = Volume / debit = 3768 / 628 = 6 menit Soal No. 9 Sebuah tabung memiliki ukuran jari-jari 14 cm dan tinggi 28 cm. Tabung tersebut berisi air setinggi 3/4 bagian. Andi memasukkan 6 buah bola besi yang masing-masing memiliki jari-jari 7 cm hingga sebagian air tumpah dari tabung. Volume air yang tumpah dari dalam tabung sebanyak. 5360 cm 3 Pembahasan Volume air yang tumpah dari tabung akan sama dengan jumlah volume 6 buah bola dan air yang ada dalam tabung dikurangi dengan volume tabung. V tumpah = 6 x Vbola + 3/4 Vtabung – Vtabung = 6Vbola – 1/4 Vtabung Sehingga: Jawaban: C Soal No. 10 Andi memiliki sebuah kerucut terbuat dari bahan yang lunak. Kerucut tersebut kemudian diiris secara horizontal tepat pada setengah ketinggian kerucut seperti pada gambar berikut. Dari hasil pemotongan yang dilakukan Andi, perbandingan volume hasil pemotongan bagian atas dengan bagian bawah adalah A. 1: 7 Pembahasan Kerucut kecil hasil potongan dan kerucut besar asalnya adalah sebangun. Dari sini dapat ditentukan perbandingan jari-jari kerucut kecil terhadap kerucut asal dan juga volumenya. Volume bagian bawah (kerucut terpancung) akan sama dengan volume kerucut sebelum dipotong dikurangi volume kerucut kecil. Dari situ dapat diperoleh perbandingan yang diminta. Misalkan tinggi kerucut asal adalah 2a dan jari-jari R, kerucut kecil tingginya separuhnya yaitu a dan jari-jari r. Perbandingan jari-jari kecil dan besar: r/R = a/2a r = 1/ 2 R Volume kerucut asal dinyatakan dalam R dan a adalah: V = 1/ 3πR 2 t V = 1/ 3πR 2(2a) V = 2/ 3πR 2a Volume kerucut kecil (potongan atas) dinyatakan dalam R dan a adalah: V = 1/ 3πr 2 t V = 1/ 3π( 1/ 2R) 2(a) V = 1/ 12πR 2a Volume kerucut terpancung (potongan bawah) dalam R dan a: Sehingga perbandingan volume bagian atas dan bagian bawah: Jawaban: D. |
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