Question 867845
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(600,600,-10,10,-10,10,(12-2x)/3,(2x-12)/3)}}}