Solve the problem.
-From a thin piece of cardboard 40 in. by 40 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.
A) 13.3 in. by 13.3 in. by 13.3 in.; 2370.4 in. ${ }^{3}$
B) 20 in. by 20 in. by 10 in.; 4000 in. $^{3}$
C)2 6.7 in. by 26.7 in. by 6.7 in.; 4740.7 in. $^{3}$
D)2 6.7 in. by 26.7 in. by 13.3 in.; 9481.5 in. ${ }^{3}$

Question

Quizplus · Accepted Answer

To maximize the volume of the box, we need to find the size of the square corners to cut out. Let x be the side length of the square corners. The volume V of the box is given by V = x(40-2x)(40-2x). By finding the derivative and setting it to zero, we find that the maximum volume occurs when x = 6.7 in. This gives dimensions of 26.7 in. by 26.7 in. by 6.7 in., resulting in a maximum volume of approximately 4740.7 in.$^3$.

Solve the Problem 3{ }^{3}3 B) 20 In by 20 In a Thin

Solve the Problem ${ }^{3}$ B) 20 In by 20 In a Thin