SOLUTION: A rectangular storage bin is to be made from a rectangular piece of sheet metal
12 cm by 10 cm, by cutting out equal corners of side x and bending up the
sides. Find x if the st
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Question 242593: A rectangular storage bin is to be made from a rectangular piece of sheet metal
12 cm by 10 cm, by cutting out equal corners of side x and bending up the
sides. Find x if the storage bin is to hold 90cm³(volume).
- I thought it might be x(120 - 4x²)= 90cm³
which I guess would be 4x³ - 120x + 90 = 0 but I'm not sure where to go from here, or even if I'm heading in the right direction.
thanks heaps
manda
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular storage bin is to be made from a rectangular piece of sheet metal
12 cm by 10 cm, by cutting out equal corners of side x and bending up the
sides.
Find x if the storage bin is to hold 90cm³(volume).
:
We know that the length and width will be decreased by 2x and height will = x
:
The volume, L * W * H:
(12-2x)(10-2x)* x = 90
(120 - 24x - 20x + 4x^2) * x = 90
which is:
x(4x^2 - 44x + 120) = 90
:
4x^3 - 44x^2 + 120x - 90 = 0
:
It's difficult to solve this for x, not being an integer solution
:
Using the graphing calc y = 4x^3 - 44x^2 + 120x - 90 = 0
:
:
Two solutions: x = 1.28cm and x = 2.39cm, either value for x will give 90 cu/cm
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