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13 August, 07:38

6. Sketch the region enclosed by the graphs of x = 0, 6y-5x=0 and x+3y=21. Find the area

7. Find the volume of the solid formed when the region is revolved around the y axis

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Answers (2)
  1. 13 August, 09:51
    0
    X = 0

    6y - 5x = 0 so it intersects x=0 at (0,0)

    x + 3y = 21

    so it intersect x=0 at (0,7)

    multiply by 2

    2x + 6y = 42

    subtracting 6y - 5x = 0

    7x = 42

    x = 6

    so the third line intersects w second line at (6,5)

    6. area of triangle = 1/2*base*height

    = 1/2*7*6

    =21

    7. volume = volume of 2 cones

    cone volume = 1/3*pi*radius^2*height

    lower cone: radius=6, height=5

    upper cone: radius=6, height=7-5=2

    volume = 1/3*pi*6^2 * (5+2)

    =84pi

    =263.89
  2. 13 August, 09:57
    0
    Given three equations, x=0

    6y-5x=0

    x+3y=21

    The lines cross at:

    x=0, y=0

    x=0, y=7

    x=6, y=5

    so base of triangle is the y-axis between 0 and 7

    height is x=6

    area=6*7/2=20.5

    volume=1/3 * (base area) * height

    =1/3 * (pi*6^2) * 7

    =84pi

    =263.9
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