Question

A rectangular sheet of cardboard measures 16cm by 6cm. Equal squares are cut out of each corner, and the sides are turned up to form an open rectangular box. What is the maximum volume of the box?

a) 360 cm³
b) 432 cm³
c) 240 cm³
d) 216 cm³

Answer 1

Step-by-step explanation:

Answer 2

To find the maximum volume of the box, we need to determine the dimensions of the squares that are cut out from the corners. By maximizing the expression (16-2x)(8-2x)x, we find that the maximum volume of the box is 14 cm³.

Step-by-step explanation:

To find the maximum volume of the box, we need to determine the dimensions of the squares that are cut out from the corners. Let's assume that the side length of each square is 'x'.

If squares are cut out from all four corners, the dimensions of the resulting box will be (16-2x) cm by (8-2x) cm by x cm. The volume of the box can be calculated by multiplying these dimensions: V = (16-2x)(8-2x)x.

To find the maximum volume, we need to maximize the expression (16-2x)(8-2x)x. We can do this by finding the critical points and determining whether they are maximum or minimum points. Differentiating the expression with respect to 'x' and setting it equal to zero, we can find the critical points. After testing these points, we find that the maximum volume occurs when x = 1 cm.

Substituting this value back into the expression, we get V = 14 cm³. Therefore, the maximum volume of the box is 14 cm³.