There are 12 students in a classroom, including the triplets joey, chloe, and zoe. If 3 of the 12 are randomly selcted to give s
1 answer:
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Answer:
Maximum volume = 649.519 cubic inches
Step-by-step explanation:
A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).
Volume is given by
V =
First, we differentiate V(x) with respect to x, to get,
Equating the first derivative to zero, we get,
Solving, with the help of quadratic formula, we get,
,
Again differentiation V(x), with respect to x, we get,
At x =
,
Thus, by double derivative test, the maxima occurs at
x = for V(x).
Thus, largest volume the box can have occurs when .
Maximum volume =
The answer is 
or (x + 1.2) ÷ 5 = 3.6
or (x + 1.2) ÷ 5 = 3.6