A rectangular sheet of cardboard 64 cm by 69 cm is used to make an open box by cutting squares of equal size from the four corners and folding up the sides. What size squares should be cut to obtain the largest possible volume?
D) 4

Question

Quizplus · Accepted Answer

Let's call the length of the side of the square cut from each corner "x". When folding up the sides to form the box, the height will also be "x". Therefore, the volume of the box can be expressed as V = x(64-2x)(69-2x).

To find the value of x that maximizes V, we can take the derivative of V with respect to x and set it equal to 0:

dV/dx = 4x^3 - 266x^2 + 4416x
0 = 4x(x-16)(x-69)

The only non-negative root of this equation is x=16. Therefore, cutting squares of size 16cm from each corner will give the largest possible volume. The answer is B.

A Rectangular Sheet of Cardboard 64 Cm by 69 Cm