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Untuk soal 7 perhatikan tabel di bawah ini. Tentukan luas permukaan dan volume tiap-tiap bangun.

Untuk soal  perhatikan tabel di bawah ini.

Tentukan luas permukaan dan volume tiap-tiap bangun.


 

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F. Ayudhita

Master Teacher

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Untuk mendapatkan nilai atau garis pelukisdigunakan konsep phytagoras pada kerucut sebagai berikut:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a. space Luas space Permukaan end cell equals cell luas space alas space tabung plus luas space selimut space tabung plus luas space selimut space kerucut end cell row blank equals cell pi r squared plus 2 pi r t plus pi r s end cell row blank equals cell pi r left parenthesis r plus 2 t plus s right parenthesis end cell end table end style      

            Untuk mendapatkan nilai begin mathsize 14px style s end style atau garis pelukis digunakan konsep phytagoras pada kerucut sebagai berikut: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell s squared end cell equals cell t squared plus r squared end cell row s equals cell square root of t squared plus r squared end root end cell end table end style  

     begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row volume equals cell volume space tabung plus volume space kerucut end cell row blank equals cell pi r to the power of 2 space end exponent t space plus 1 third pi r squared t end cell row blank equals cell 4 over 3 pi r squared t end cell end table end style  

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight b. space Luas space permukaan end cell equals cell 2 cross times space luas space selimut space kerucut space plus luas space selimut space tabung end cell row blank equals cell 2 cross times pi r s plus 2 pi r t end cell row blank equals cell 2 pi r s plus 2 pi r t end cell row blank equals cell 2 pi r open parentheses s plus t close parentheses end cell end table end style 

 

    begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row Volume equals cell 2 cross times volume space kerucut plus volume space tabung end cell row blank equals cell 2 cross times 1 third pi r squared t plus pi r squared t end cell row blank equals cell 2 over 3 pi r squared t plus pi r squared t space end cell row blank equals cell left parenthesis 2 over 3 plus 1 right parenthesis pi r squared t end cell row blank equals cell 5 over 3 pi r squared t end cell end table end style  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight c. space Luas space permukaan end cell equals cell 1 half luas space permukaan space bola space plus space luas space selimut space kerucut end cell row blank equals cell 1 half cross times 4 pi r squared plus pi r s end cell row blank equals cell 2 pi r squared plus pi r s end cell row blank equals cell pi r open parentheses 2 r plus s close parentheses end cell end table end style 

 

     begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row Volume equals cell 1 half volume space bola plus volume space kerucut end cell row blank equals cell 1 half cross times 4 over 3 pi r cubed plus 1 third pi r squared t end cell row blank equals cell 2 over 3 pi r cubed plus 1 third pi r squared t end cell row blank equals cell 1 third pi r squared left parenthesis 2 r plus t right parenthesis end cell end table end style   

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell d. Luas space Permukaan end cell equals cell 1 half Luas space permukaan space bola plus luas space selimut space tabung plus luas space tutup space tabung end cell row blank equals cell 1 half cross times 4 pi r squared plus 2 pi r t plus pi r squared end cell row blank equals cell 2 pi r squared plus 2 pi r t plus pi r squared end cell row blank equals cell 3 pi r squared plus 2 pi r t end cell row blank equals cell pi r open parentheses 3 r plus 2 t close parentheses end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Volume space end cell equals cell 1 half Volume space bola plus volume space tabung end cell row blank equals cell 1 half cross times 4 over 3 pi r cubed plus pi r squared t end cell row blank equals cell 2 over 3 pi r cubed plus pi r squared t end cell row blank equals cell pi r squared open parentheses 2 over 3 r plus t close parentheses end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight e. space Luas space Permukaan space end cell equals cell 1 half space luas space permukaan space bola space plus space luas space selimut space tabung space plus luas space selimut space kerucut end cell row blank equals cell 1 half cross times 4 pi r squared plus 2 pi r t plus pi r s end cell row blank equals cell 2 pi r squared plus 2 pi r t plus pi r s end cell row blank equals cell pi r open parentheses 2 r plus 2 t plus s close parentheses end cell end table end style 

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row Volume equals cell 1 half volume space bola plus volume space tabung plus volume space kerucut end cell row blank equals cell 1 half cross times 4 over 3 pi r cubed plus pi r squared t plus 1 third pi r squared t end cell row blank equals cell 2 over 3 pi r cubed plus pi r squared t plus 1 third pi r squared t end cell row blank equals cell pi r squared left parenthesis 2 over 3 r plus 4 over 3 t right parenthesis end cell row blank equals cell 2 over 3 pi r squared left parenthesis r plus 2 t right parenthesis end cell end table end style   

 

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begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row volume equals cell 2 cross times 1 half volume space bola plus volume space tabung end cell row blank equals cell 4 over 3 pi r cubed plus pi r squared t end cell row blank equals cell pi r squared open parentheses 4 over 3 r plus t close parentheses end cell end table end style

 

 

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