let the dimensions of the rectangle be x and y.
Folding the x-side, we have a triangle with sides x/3, and height (x/3)(√3/2) = x/(2√3)
he volume of the prism is thus
v = 1/2 (x/3) x/(2√3) y = x^2 y / (12√3)
Now, 2(x+y) = 30, so
y = 15-x, and we have
v = x^2(15-x)/(12√3)
we want to find x so v is a maximum
dv/dx = 3x(10-x) / (12√3) = x(10-x)/(4√3)
dv/dx = 0 when x = 0 or 10
So, the rectangle is 10 x 5, and we fold the 10" side into thirds.
in a rectangular with a perimeter of 30 inches two parallel and equally spaced creases are made the cardboard is then folded to make a triangular prism with open ends that are equilateral triangles you will maximize the volume
how do i solve this?
1 answer
1 answer