O adalah pusat lingkaran dengan panjang busur MN = 6π cm dan luas juring OMN = 27π cm^2. Panjang jari-jari ON adalah .... A. 9cm B. 7,5 cm C. 6 cm D. 4,5 cm

<p>Halo Luna. Kakak bantu jawab ya.</p><p>Jawab: A</p><p>Pembahasan:</p><p>Ingat!</p><ul><li>Luas juring OMN = (𝞱/360°)×𝞹r²</li><li>Panjang busur MN = (𝞱/360°)×2𝞹r</li></ul><p>Dengan menggunakan konsep di atas, diperoleh</p><p>Luas juring OMN = 27𝞹</p><p>&nbsp; &nbsp; &nbsp; &nbsp; (𝞱/360°)×𝞹r² = 27𝞹</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(𝞱/360°)×r² = 27 (kedua ruas dibagi 𝞹)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(𝞱/360°) = 27/r²</p><p>Panjang busur MN = 6𝞹</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(𝞱/360°)×2𝞹r = 6𝞹</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(𝞱/360°)×2r = 6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (𝞱/360°) = 6/2r</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (𝞱/360°) = 3/r</p><p>Perhatikan bahwa:</p><p>(𝞱/360°) = (𝞱/360°)</p><p>&nbsp; &nbsp; &nbsp; &nbsp;27/r²= 3/r</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 27r = 3r²</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 27 = 3r (kedua ruas dibagi r)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; 27/3 = r</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;9 = r</p><p>Oleh karena itu, panjang jari-jari lingkaran adalah 9 cm.</p><p>&nbsp;</p><p><strong><u>Jadi, jawaban yang benar adalah A.</u></strong></p>