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Question
An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal square from the corner and turning up the side as shown. Express the volume V of the box as a function of x
Solution
After cutting squares we will get a cuboid,
length of the cuboid (l) = 24 – 2x
breadth of the cuboid (b) = 24 – 2x
height of the cuboid (h) = 2x
Volume of the box = Volume of the cuboid
V = (24 – 2x)(24 – 2x) (x)
= (24 – 2x)2 (x)
= (576 + 4x2 – 96x) x
= 576x + 4x3 – 96x2
V = 4x3 – 96x2 + 576x
V(x) = 4x3 – 96x2 + 576x
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