SOLUTION: The points of intersection of the line 2x+3y=12 with the x-axis and the y-axis are the endpoints of a segment. To the nearest hundredth, what is the volume of the cone formed by ro

Algebra ->  Volume -> SOLUTION: The points of intersection of the line 2x+3y=12 with the x-axis and the y-axis are the endpoints of a segment. To the nearest hundredth, what is the volume of the cone formed by ro      Log On


   

Question 867845: The points of intersection of the line 2x+3y=12 with the x-axis and the y-axis are the endpoints of a segment. To the nearest hundredth, what is the volume of the cone formed by rotating that segment around the x-axis ?
A. 24 units3
B. 100.53 units3
C. 150.72 units3
D. 401.92 units3
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the equation is 2x + 3y = 12
when x = 0, the equation becomes 3y = 12 and you get y = 4
when y = 0, the equation becomes 2x = 12 and you get x = 6
the height of the cone will be 6 and the radius of the cone will be 4.
the volume of a cone is equal to 1/3 * pi * r^2 * h
that becomes 1/3 * pi * 4^2 * 6 which becomes 1/3 * pi * 16 * 6 which becomes pi * 16 * 2 which becomes 32 * pi which is roughly equal to 100.53 cubic units.
A graph of the line is shown below:
the equation for the other side of the cone is 2x - 3y = 12
graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%2812-2x%29%2F3%2C%282x-12%29%2F3%29