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Berisi bangun-bangun ruang 3 dimensi.
Typology: Lecture notes
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1 3 𝑥 𝑗𝑢𝑚𝑙𝑎ℎ 𝑘𝑒𝑡𝑖𝑔𝑎 𝑟𝑢𝑠𝑢𝑘 𝑡𝑒𝑔𝑎𝑘 𝑥 𝑙𝑢𝑎𝑠 𝑎𝑙𝑎𝑠 =^
1 3 (𝑡𝐷^ + 𝑡𝐸^ + 𝑡𝐹^ )𝐿∆𝐴𝐵𝐶
Karena luas selubung merupakan jumlah luas 4 trapesium yang sama besar, maka terlebih dahulu mencari t bagian trapesium :
Garis yang dimaksud adalah garis AB dan garis tersebut melalui (t,r) dengan gradien 𝑟 𝑡 , maka dari persamaan garis umum (𝑦 − 𝑦 1 ) = 𝑚(𝑥 − 𝑥 1 ) Sehingga diperoleh (𝑦 − 𝑟) = 𝑟 𝑡 (𝑥 − 𝑡) 𝑡(𝑦 − 𝑟) = 𝑟(𝑥 − 𝑡) 𝑡𝑦 − 𝑡𝑟 = 𝑟𝑥 − 𝑟𝑡 𝑡𝑦 = 𝑟𝑥 − 𝑟𝑡 + 𝑡𝑟 𝑡𝑦 = 𝑟𝑥 𝑦 =
Selanjutnya hitung dengan integral dengan selang [0,t]
𝑉 = 𝜋 ∫ 𝑦^2
𝑡
0
Luas permukaan : 2𝜋𝑅𝑡 Volume : 13 𝜋𝑡^2 (3𝑅 − 𝑡)
Luas permukaan : 2𝜋𝑅𝑡 Volume : 16 𝜋𝑡𝑘^2 𝑑𝑖𝑚𝑎𝑛𝑎 𝑘 = 𝑎𝑝𝑜𝑡𝑒𝑚𝑎, 𝑘 = √𝑟 12 + 𝑡^2.