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Suatu kerucut memiliki jari-jari  dan tinggi . Jika luas permukaan kerucut adalah  dan volume kerucut adalah  maka tentukan: b. Nilai dari

Pertanyaan

Suatu kerucut memiliki jari-jari begin mathsize 14px style 6 space cm end style dan tinggi begin mathsize 14px style straight t space cm end style. Jika luas permukaan kerucut adalah begin mathsize 14px style straight A space cm squared end style dan volume kerucut adalah begin mathsize 14px style straight A space cm cubed end style maka tentukan:

b. Nilai dari begin mathsize 14px style straight A end style 

Pembahasan Soal:

Diketaui kerucut dengan ukuranbegin mathsize 14px style r equals 6 space cm end style, begin mathsize 14px style t equals t space cm end style, begin mathsize 14px style L equals A space cm squared end style dan begin mathsize 14px style V equals A space cm cubed end style, maka:

begin mathsize 14px style s squared equals r squared plus t squared s equals plus-or-minus square root of r squared plus t squared end root end style

Karena panjang garis pelukis kerucut tidak mungkin negatif, maka yang memenuhi adalah begin mathsize 14px style s equals square root of r squared plus t squared end root end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell L equals πr left parenthesis straight r plus straight s right parenthesis A equals straight pi cross times 6 cross times open parentheses 6 plus square root of 6 squared plus straight t squared end root close parentheses end cell row A equals cell 36 straight pi plus 6 straight pi square root of 36 plus straight t squared end root end cell row blank blank blank row straight V equals cell 1 third πr squared straight t end cell row straight A equals cell 1 third straight pi cross times 6 squared cross times straight t end cell row straight A equals cell 12 πt end cell row cell 36 up diagonal strike straight pi plus 6 up diagonal strike straight pi square root of 36 plus straight t squared end root end cell equals cell 12 up diagonal strike straight pi straight t space left parenthesis kedua space ruas space divided by 6 right parenthesis end cell row cell 6 plus square root of 36 plus straight t squared end root end cell equals cell 2 straight t end cell row cell square root of 36 plus straight t squared end root end cell equals cell 2 straight t minus 6 space left parenthesis kedua space ruas space dikuadratkan right parenthesis end cell row cell 36 plus straight t squared end cell equals cell 4 straight t squared minus 24 straight t plus 36 end cell row cell 4 straight t squared minus 24 straight t plus 36 minus 36 minus straight t squared end cell equals 0 row cell 3 straight t squared minus 24 straight t end cell equals cell 0 space left parenthesis kedua space ruas space divided by 3 right parenthesis end cell row cell straight t squared minus 8 straight t end cell equals 0 row straight t equals cell 0 space atau space straight t equals 8 end cell end table end style 

Karena tinggi kerucut tidak mungkin bernilai 0, maka yang memenuhi adalah begin mathsize 14px style t equals 8 space cm end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row V equals cell 1 third πr squared straight t end cell row cell straight A space cm cubed end cell equals cell 1 third cross times 3 comma 14 cross times open parentheses 6 space cm close parentheses squared cross times 8 space cm end cell row cell straight A up diagonal strike space cm cubed end strike end cell equals cell 301 comma 44 space up diagonal strike cm cubed end strike end cell row straight A equals cell 301 comma 44 end cell end table end style 

Jadi, nilai A adalah begin mathsize 14px style 301 comma 44 end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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