Sebuah kerucut mempunyai volume 27cm3. Jika diameter kerucut diperbesar 3 kali dan tingginya diperbesar 2 kali, maka volume keucut tersebut adalah ...

Pertanyaan

Sebuah kerucut mempunyai volume $\style{font-size:14px}{27\;\mathrm{cm}^3}$ . Jika diameter kerucut diperbesar 3 kali dan tingginya diperbesar 2 kali, maka volume keucut tersebut adalah ...

$begin mathsize 14px style 972 space cm cubed end style$
$begin mathsize 14px style 486 space cm cubed end style$
$begin mathsize 14px style 324 space cm cubed end style$
$begin mathsize 14px style 162 space cm cubed end style$

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight V subscript 1 end cell equals cell 27 space cm cubed end cell row cell straight d subscript 2 end cell equals cell 3 straight d subscript 1 end cell row cell straight t subscript 2 end cell equals cell 2 straight t subscript 2 end cell end table end style$

Dengan menggunakan perbandingan volume kerucut, diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight V subscript 1 over straight V subscript 2 end cell equals cell fraction numerator begin display style 1 third end style times open parentheses begin display style 1 fourth end style straight pi straight d subscript 1 close parentheses squared times straight t subscript 1 over denominator begin display style 1 third end style times open parentheses begin display style 1 fourth end style πd subscript 2 close parentheses squared times straight t subscript 2 end fraction end cell row cell 27 over straight V subscript 2 end cell equals cell fraction numerator begin display style 1 over 16 end style times straight pi squared times straight d subscript 1 superscript 2 times straight t subscript 1 over denominator begin display style 1 over 16 end style times straight pi squared times straight d subscript 2 superscript 2 times open parentheses 2 straight t subscript 1 close parentheses end fraction end cell row cell 27 over straight V subscript 2 end cell equals cell fraction numerator straight d subscript 1 squared over denominator open parentheses 3 straight d subscript 1 close parentheses squared times 2 end fraction end cell row cell 27 over straight V subscript 2 end cell equals cell fraction numerator straight d subscript 1 squared over denominator 9 times straight d subscript 1 squared times 2 end fraction space end cell row cell 27 over straight V subscript 2 end cell equals cell 1 over 18 end cell row cell straight V subscript 2 end cell equals cell 27 cross times 18 end cell row cell straight V subscript 2 end cell equals cell 486 space cm cubed end cell end table end style$

Jadi jawaban yang tepat adalah B

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Freelancer9

Terakhir diupdate 06 Oktober 2021