Question -
Answer -
Let the side of the square to be cut offbe x cm. Then, the height of the box is x, thelength is 45 − 2x, and the breadth is 24 − 2x.
Therefore, the volume V(x)of the box is given by,
Now,
.
x = 18and x = 5
It is not possible to cut off a square ofside 18 cm from each corner of the rectangular sheet. Thus, x cannotbe equal to 18.
∴x = 5
Now,
.
By second derivative test, x =5 is the point of maxima.Hence, the side of the square to be cut off to make thevolume of the box maximum possible is 5 cm.