a) correct
b) correct, but do you know why the volume is zero ?
c) this will also answer part b)
the given volume = c(8.5-2c)(11-2c) in expanded form
notice if c = 4.25, the size of the cut-out, you would be cutting away 4.25 on each side of the width
but the width is only 8.5.
So by cutting away 4.25 on each end of the 8.5, you would have no width left for the base of the box
the dimensions of the box would be
0 by (11 -2(4/25) by 4/25 which of course gives us a zero.
notice that in my factored form of the equation, there would be a restriction of
0 < c < 4.25
A piece of 8.5-by-11-inch cardboard has identical squares cut from its corners. It is then folded into a box with no lid. The volume of the box in cubic inches is 4c^3 - 39c^2 + 93.5c, where c is the side length of the missing squares in inches.
a. What is the volume of the box if c =1 in.?
A: 58.5?
b. What is the volume of the box if c = 4.25 in.?
A: 0.
c. Does your answer to part c make sense? Explain why or why not.
A: Yes, because it is solved by order of operations? (I am not entirely certain.)
1 answer
1 answer