Matematika

Pertanyaan

bisa bantuin kawand.... no 10 B kerucut didalam bola
bisa bantuin kawand.... no 10 B kerucut didalam bola

1 Jawaban

  • Kerucut DaLam boLa

    Penampang bola ketika dibelah tepat ditengah ---> lingkaran

    Penampang kerucut ---> segitiga (∆ABC)

    AB = BC = 16 cm
    sudut ABC = x

    r bola = AO = OC = 10 cm
    sudut AOC = 2x

    AC = diameter kerucut

    AC² = AC²
    AB² + BC² - 2. AB . BC cos x = AO² + OC² - 2 AO OC cos 2x
    16² + 16² - 2. 16.16 cos x = 10² + 10² - 2.10.10 cos 2x
    200 cos 2x - 512 cos x + 312 = 0
    25 cos 2x - 64 cos x + 39 = 0
    25(2 cos² x - 1) - 64 cos x + 39 = 0
    25 cos² x - 32 cos x + 7 = 0
    (25 cos x - 7)(cos x - 1) = 0

    yg memenuhi :
    cos x = 7/25
    sin x = 24/25

    r = (AB × BC × AC) / (4 × L.ABC)
    r = (AB × BC × AC) / (4 × 1/2 × AB × BC × sin x)
    r = AC / (2 sin x)
    AC = 10 × 2 × 24/25
    AC = 19,2 cm

    jari2 kerucut
    = 1/2 AC
    = 9,6 cm ✔