Matematika

Pertanyaan

Tolong bantuan nya nomor 4
Tolong bantuan nya nomor 4

1 Jawaban

  • titik potong terhadap sumbu x diperoleh jika y = 0
    (x - 5)^2 + y^2 = 25
    (x - 5)^2 + 0^2 = 25
    (x - 5) = ± 5
    x = 5 ± 5
    x = 10 atau x = 0 => batas integral

    (x - 5)^2 + y^2 = 25
    y^2 = 25 - (x - 5)^2
    V = π (batas 0 - 10) ∫ y^2 dx
    = π (batas 0 - 10) ∫ 25 - (x - 5)^2 dx
    = π (25x - 1/3 (x - 5)^3) | batas 0 - 10
    = π [(25 (10) - 1/3 (10 - 5)^3) - (25(0) - 1/3 (0 - 5)^3))
    = π [250 - 125/3 - (0 + 125/3)]
    = (250 - 250/3) π
    = (750 - 250)/3 π
    = (500π)/3

    Atau bisa juga dengan rumus volume bola dengan r = 5
    V = 4/3 π r^3 = 4/3 π (5)^3 = 4/3 π (125) = (500π)/3