So what we do is area that remains=total area-triangle area that was cut out
we need to find 2 things total area triangle area
total area=rectange=base times height area=(3x+4) times (2x+3) FOIL or distribute 6x^2+8x+9x+12=6x^2+17x+12
triangle area=1/2 times base times height triangle area=1/2 times (2x+2) times (x-2)= (x+2) times (x-2)=x^2+2x-2x-4=x^2-4
so total area=6x^2+17x+12 triangle area=x^2-4
subtract area that remains=total area-triangle area that was cut out area that remains=6x^2+17x+12-(x^2-4)= 6x^2+17x+12-x^2+4= 6x^2-x^2+17x+12+4= 5x^2+17x+16
We know that the volume of a cone is given by the following relation: V = (pi * r^2 * h)/3 where r is radius and h is height of the cone In our case, radius is diameter divide by 2: V = (pi * (8/2)^2 * 10) / 3 = 167.55 cubic inches So the container holds 167.55 cubic inches
