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 th

Question

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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2022-04-16T17:13:44+00:00 2 Answers 0

Answers ( 2 )

  1. Aubrey
    0
    2022-04-16T17:14:48+00:00

    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

  2. Valerie
    0
    2022-04-16T17:15:28+00:00

    x = 0

    6y – 5x = 0so 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

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