liubitsaghn2145
27.12.2019 •
Mathematics
You cut square corners from a piece of cardboard that has dimensions 32 cm by 40 cm. you then fold the cardboard to create a box with no lid. to the nearest centimeter, what are the dimensions of the box that will have the greatest volume?
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Ответ:
h = 6 cm
l = (32-2(6)) = 20 cm
w = (40-2(6)) = 28 cm
Step-by-step explanation:
Given in the question a piece of cardboard having dimensions 32 by 40
Suppose we cut square of length x
When you cut square corners from a piece of cardboard, two sides are 32-2x, and other two sides are 40-2x lengths
Step 1Formula for the volume of box
v = height * length * width
v = x (32-2x) (40-2x)
v = 4x³ - 144x² + 1280x
Step 2Find derivative and equal it to 0
dv/dx = 4(3)x² - (2)144x + 1280
0 = 12x² - 288x + 1280
x1 = 18.110
x2 =5.88
Step 3Select x and plug value of x to find dimension
(32-2x) > 0
2x < 32
x < 16
so domain say that x should be less than 16 which means x = 5.88 ≈ 6 cm
h = 6 cm
l = (32-2(6)) = 20 cm
w = (40-2(6)) = 28 cm
Ответ:
Thanks
Step-by-step explanation: