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SMK Teknologi dan Rekayasa

Soal 132 Volume Benda Putar


Volume\ benda\ putar\ yang\ terjadi\ jika\ daerah\ yang\ dibatasi\ oleh\ kurva\\y=x+2\ dan\ sumbu\ X\ diputar\ 360^{\circ}\ mengelilingi\ sumbu\ X\ dari\\x=0\ sampai\ x=2\ adalah\ ....
a.\ \ 18\frac{2}{3}\pi \ satuan\ volume\\ \\b.\ \ 20\frac{1}{2}\pi \ satuan\ volume\\ \\c.\ \ 21\frac{3}{5}\pi \ satuan\ volume\\ \\d.\ \ 19\frac{2}{5}\pi \ satuan\ volume\\ \\e.\ \ 20\frac{2}{3}\pi \ satuan\ volume
Jawaban: a


Karena\ pemutaran\ mengelilingi\ sumbu\ X,\ maka:
Volume\ benda\ putar=\pi \int_{a}^{b}y^{2}\ dx=\pi \int_{0}^{2}(x+2)^{2}\ dx
\begin{array}{rcl}Misalkan\ u=x+2&\to &du=(1+0)\ dx=dx\\Untuk\ x=0&\to &u=0+2=2\\Untuk\ x=2&\to &u=2+2=4\end{array}

\begin{array}{rcl}Volume\ benda\ putar&=&\pi \int_{2}^{4}u^{2}\ du\\\\&=&\pi \left [ \frac{u^{3}}{3} \right ]_{2}^{4}\\\\&=&\frac{1}{3}\pi \left [ u^{3} \right ]_{2}^{4}\\\\&=&\frac{1}{3}\pi \left [ 4^{3}-2^{3} \right ]\\\\&=&\frac{1}{3}\pi \left [ 64-8 \right ]\\\\&=&\frac{1}{3}\pi \times 56\\\\&=&18\frac{2}{3}\pi \end{array}

About Kalakay

Guru Matematika SMK

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One thought on “Soal 132 Volume Benda Putar

  1. mantep gan sangat membantu dan menambah ilmu tentang volume benda putar..

    Posted by vikri | 14 Juni 2012, 7:04 PM

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