Answer:
The maximum possible volume = 332.685 cubic inches
Step-by-step explanation:
From the information given:
Let the height be = x
The length be = 24 - 2x
The width be = 12 - 2x
Then V = x (24 -2x) ( 12 - 2x)
V = x ( 288 -48x - 24x +4x²)
V = x(288 - 72x + 4x²)
V = 288x - 72x² + 4x³
where;
∴
x = 2.536 ( since the length cannot be negative)
So, the length x = 24 - 2(2.535) = 18.93
The width = 12 - 2(2.535) = 6.93
heigth = 2.536
∴
V = 18.93 × 6.93 × 2.536
V = 332.685 cubic inches
