As shown in the figure, a small square with a side length of 2 √ 2cm is cut off at the four corners of the square cardboard with a side length of (20 √ 3-6 √ 2) cm, and then folded along the dotted line to form a carton without cover, and the volume of the carton is calculated

As shown in the figure, a small square with a side length of 2 √ 2cm is cut off at the four corners of the square cardboard with a side length of (20 √ 3-6 √ 2) cm, and then folded along the dotted line to form a carton without cover, and the volume of the carton is calculated


Bottom side length 20 √ 3-6 √ 2-2 × 2 √ 2 = 20 √ 3-10 √ 2
So the volume is (20 √ 3-10 √ 2) &# 178; × 2 √ 2
=(1200-400√6+200)×2√2
=2800 √ 2-1600 √ 3cm



Subtract a square with side length of X (CM) from the four corners of a rectangular piece of hard paper with length of 20cm and width of 16cm
Subtract a square with side length of X (CM) from the four corners of a rectangular piece of hard paper with length of 20cm and width of 16cm, and then make a carton without cover. Express the volume and surface area of the carton with algebraic formula. And calculate the volume and surface area of the carton when x = 2 (CM)?


Volume = x (20-2x) (16-2x)
=X(320-72X+4X2)
=4X3-72X2+320X
Surface area = 20 × 16-4x2
=320-4X2