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Diketahui prisma segitiga tegak ABC.DEF. Panjang ,...

Diketahui prisma segitiga tegak ABC.DEF. Panjang begin mathsize 14px style AB equals 4 space cm end style, begin mathsize 14px style BC equals 6 space cm end style, begin mathsize 14px style AC equals 2 square root of 7 space end root cm end style dan begin mathsize 14px style CF equals 8 space cm end style. Volume prisma tersebut adalah..

  1. begin mathsize 14px style 96 square root of 3 space cm cubed end style

  2. begin mathsize 14px style 96 square root of 2 space cm cubed end style

  3. begin mathsize 14px style 96 space cm cubed end style

  4. begin mathsize 14px style 48 space square root of 3 space cm cubed end style

  5. begin mathsize 14px style 48 square root of 2 space cm cubed end style

Jawaban:

Diketahui:

sisi-sisi pada alas segitiga yaitu:

begin mathsize 14px style AB equals 4 space cm end style

begin mathsize 14px style BC equals 6 space cm end style

begin mathsize 14px style AC equals 2 square root of 7 space end root cm end style

begin mathsize 14px style tinggi space prisma equals CF equals 8 space cm end style

Ditanyakan:

Volume prisma tersebut adalah...

Penyelesaian:

Pertama kita tentukan luas alas dari segitiga pada prisma tersebut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight s equals cell 1 half space keliling space segitiga end cell row straight s equals cell 1 half cross times open parentheses 4 plus 6 plus 2 square root of 7 close parentheses end cell row straight s equals cell 5 plus square root of 7 end cell row straight L equals cell square root of straight s open parentheses straight s minus straight a close parentheses open parentheses straight s minus straight b close parentheses open parentheses straight s minus straight c close parentheses end root end cell row straight L equals cell square root of open parentheses 5 plus square root of 7 close parentheses open parentheses 5 plus square root of 7 minus 4 close parentheses open parentheses 5 plus square root of 7 minus 6 close parentheses open parentheses 5 plus square root of 7 minus 2 square root of 7 close parentheses end root end cell row straight L equals cell square root of open parentheses 5 plus square root of 7 close parentheses open parentheses 5 minus square root of 7 close parentheses open parentheses 1 plus square root of 7 close parentheses open parentheses negative 1 plus square root of 7 close parentheses end root end cell row straight L equals cell square root of open parentheses 25 minus 7 close parentheses open parentheses 7 minus 1 close parentheses end root end cell row straight L equals cell square root of 18 cross times 6 end root end cell row straight L equals cell 6 square root of 3 space cm squared end cell end table end style

Sehingga Volume prisma tersebut adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight V equals cell Luas space alas cross times tinggi end cell row blank equals cell 6 square root of 3 cross times 8 end cell row blank equals cell 48 square root of 3 space cm cubed end cell end table end style

Jadi, jawaban yang tepat adalah D

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