a company wants to design a cylindrical object that has a height of 10 centimeters and a volume of at least 2,000 cubic centimet
1 answer:
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Answer:
All the sizes that satisfy
Step-by-step explanation:
To answer this question we first need to find the minimum wasted area of the dough.
Let us call the diameter of the cookie , and
the length of the dough sheet, then the
number of cookies that fit into length
will be
and therefore, the number that will fit into the whole square sheet will be
Since the area of each cookie is
the area of n^2 cookies will be
,
which is the area of all the cookies cut out from the dough sheet; therefore, after the cutting, the area left will be
(1).
putting in the value of we get
which simplifies to
area left = a^2( 1 - (π/4))
putting in a = 12 we get
area left = 30.902 in^2.
Going back to equation (1) we find that
a^2-n^2(πd^2/4) =30.902
12^2- n^2(πd^2/4) =30.902
and if we call k = n^2, we get
12^2- k(πd^2/4) =30.902
113.098 = k(πd^2/4)
simplifiying this gives
kd^2 = 144.
As a reminder, k here is the number of cookies cut from the dough sheet.
Hence, our cookie diameter must satisfy kd^2 = 144,<em> meaning larger the diameter of the cookies less of the should you cut out to satisfy the above equality. </em>