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angeline2004
16.11.2019 •
Mathematics
Find the radius and height of a cylindrical soda can with a volume of 256cm^3 that minimize the surface area.
b: compare your answer in part a to a real soda can, which has a volume of 256cm^3, a radius of 2.8 cm, and a height of 10.7 cm, to conclude that real soda cans do not seem to have an optimal design. then use the fact that real soda cans have a double thickness in their top and bottom surfaces to find the radius and height that minimizes the surface area of a real can (the surface area of the top and bottom are now twice their values in part a.
b: new radius=?
new height=?
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Ответ:
A) Radius: 3.44 cm.
Height: 6.88 cm.
B) Radius: 2.73 cm.
Height: 10.92 cm.
Step-by-step explanation:
We have to solve a optimization problem with constraints. The surface area has to be minimized, restrained to a fixed volumen.
a) We can express the volume of the soda can as:
This is the constraint.
The function we want to minimize is the surface, and it can be expressed as:
To solve this, we can express h in function of r:
And replace it in the surface equation
To optimize the function, we derive and equal to zero
The radius that minimizes the surface is r=3.44 cm.
The height is then
The height that minimizes the surface is h=6.88 cm.
b) The new equation for the real surface is:
We derive and equal to zero
The radius that minimizes the real surface is r=2.73 cm.
The height is then
The height that minimizes the real surface is h=10.92 cm.
Ответ:
0.763
Step-by-step explanation:
its easy just add a 0 and a . before the number