Coba dijawab pertanyaan populer berikut. Dari segitiga ABC diketahui AB= 3cm, sudut B= 120°, BC= 4cm.... Question from @Dimastoro

December 2018 1 55 Report

Coba dijawab pertanyaan populer berikut. Dari segitiga ABC diketahui AB= 3cm, sudut B= 120°, BC= 4cm. Segitiga ABC diputar mengelilingi AB. Hitunglah volume dan luas putaran yang terjadi.

izharulhaq78 $\displaystyle\text{Apabila ABC diputar mengelilingi AB, maka akan terbentuk}\\\text{kerucut}\\\\\text{Perhatikan lampiran}\\\\\text{OB}=\text{BC}\cos(180-\theta)\\\text{OB}=4\cos(180-120)\\\text{OB}=4\cos60\\\text{OB}=2\\\\\text{OC}=\text{BC}\sin(180-\theta)\\\text{OC}=4\sin(180-120)\\\text{OC}=4\sin60\\\text{OC}=2\sqrt3\\\\\text{AC}^2=\text{AO}^2+\text{OC}^2\\\text{AC}^2=(\text{AB+OB})^2+\text{OC}^2\\\text{AC}^2=5^2+(2\sqrt3)^2\\\text{AC}^2=25+12\\\text{AC}=\sqrt{37}$

$\displaystyle \text{Cari Volume kerucut}\\V=V_\text{I}-V_\text{II}\\V=\frac{1}{3}\pi r_1^2t_1-\frac{1}{3}\pi r_2^2t_2\\V=\frac{1}{3}\pi((\text{OC})^2\text{AO}-(\text{OC})^2\text{OB})\\V=\frac{1}{3}\pi\text{OC}^2(\text{AO}-\text{OB})\\V=\frac{1}{3}\pi(2\sqrt3)^2(5-2)\\V=\frac{1}{3}\pi(12)(3)\\\boxed{\boxed{V=12\pi\,\text{cm}^3}}$

$\displaystyle \text{Cari luas permukaan}\\A=A_\text{I}+A_\text{II}\\A=\pi r_1s_1+\pi r_2s_2\\A=\pi(\text{OC}\cdot\text{AC}+\text{OC}\cdot\text{BC})\\A=\pi\text{OC}(\text{AC}+\text{BC})\\A=\pi\cdot2
\sqrt3(\sqrt{37}+4)\\\boxed{\boxed{A=(2\pi\sqrt{111}+8\pi\sqrt3)\,\text{cm}^2}}$

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