Answer:
70 m^2
Step-by-step explanation:
The key shows that each square side on the grid measures 2 m. The base of the triangle measures 7 grid square sides, so it measures 14 m. The height of the triangle measures 5 grid square sides, so it measures 10 m.
area of triangle = bh/2
area = (14 m)(10 m)/2
area = 140 m^2/2
area = 70 m^2
V=x(8-2x)(10-2x) or expanded
V=x(4x^2-36x+80)
V=4x^3-36x^2+80x
...
If you were to graph the above equation for V(x) you will see a maximum point where the "y" value is maximized, but be careful as V will increase without bound at values of x that are not part of the domain, ie, in this case x<8/2, x<4 to have any meaning...The proper domain of this function is:
x=(0,4), Mathematically finding this point quickly is by differentiating it with respect to x...
dV/dx=12x^2-72x+80, The maximum volume will occur when dV/dx=0 and the x value is within the correct domain...
12x^2-72x+80=0 (using the quadratic formula for ease)
x=(72±√1344)/24, and since x<4
x≈1.472in (to the nearest one thousandth of an inch)
