WEBVTT
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we have a question and this acorn shaped paper drinking
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cup is to be made to hold 26 27 centimeter
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cube. So this is the corn. Okay find
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the height and radius of the cup so that with
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the smallest amount of paper, if this is the
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height, This is the radius. So volume bill
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is one x 3 by our cue, one x
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3 buyers Square H. This is the volume And
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volume is being given as 27 centimetre q. So
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27 will be equal to one x 3. Fire
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square H. So let us say that will be
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equal 27-381 by by R squared. Okay now we
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have to maximize or minimize the total surface area total
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surface area. So here there will be no base
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because it is a cup so called surface area.
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So curve surface area there is a C will be
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equal to by uh L so here by R.
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L will be equal to at the square place are
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square on the route at a square plus r squared
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and that's all. Okay so here we could have
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found out at the square And so we are square
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. Just for the sake of simplicity. Square is
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81 by buy it. And this is a clip
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again we can get sequel to by our into yeah
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At a square plus our Square 81 by by H
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and are here This is also our I will be
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nine by under route By H and two At the
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Squire by 81 by by H. Okay So if
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you could just take it inside it will be nine
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at the Squire. So at by bye. Bless
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85. When bye by square at the square.
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Okay. So now we have to differentiate this and
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we know that if we have to maximize or minimize
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this function see? So let us take this only
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and we can do rest of them. So let
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us say this function is uh an ach equal to
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catch by pi Plus 81 by by a square.
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It's square. So to maximize minimize and for critical
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point of that that should be equal to zero.
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So one by pi. Uh huh. Plus.
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Okay let us write that at by pi Plus 81
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by Pi Square at the rest of the par-2
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. So bless 81 by Pi Square-2 as opposed
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to the par-3. Okay, so they should
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be equal to zero which means one by pi place
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162 But by a square excuse should be equal to
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zero. Okay uh This should be negative. So
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162 by By Square. HQ should be equal to
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one by PI. Mhm Which means that you will
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be equal to 162 by Pi. So it will
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be equal to 162 by by raised to the power
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one x 3. So this is the value of
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it. No to get the value of our From
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here we can get the value of our to our
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square is eight. Even by pi at our square
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is 81. Bye. Buy into 162. My
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pie one x 3. So this is 81 by
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buy into one by pirates. The part one by
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31 day 62 raised the part one by three.
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Yeah so this is 81 by pirates to the power
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To buy 3 162. Mhm 333 333. So
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here it will be yeah three In 2 3 days
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to the part one x 3. So this is
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27 which is three cube by pirates with the power
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to buy three trillions department by three. So are
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square will be equal to uh previous to the power
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eight by three Divide by pirates to the power to
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buy three. So I will be equal to the
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square root of three years to the power 813.
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Pirates with power to buy three one by two.
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So our will be equal to three days to the
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power four by three divide by pirates to the power
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one by three. So this is three In 2
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, 3 days to the part one by three divided
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by pirates to the parliament by three. So we
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have our which is equal to three and 23 by
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pi raised to the power one by three And h
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equals two 162 by pirates to the power on by
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three. Mhm. Ach is 162 by five years
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to the power one by three. Uh So this
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is three days to the power. Uh huh.
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Well the and nine. So simply this will be
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equal to three years to power 33 to 1 by
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three Pirates Department by three. Okay, so actually
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equal to three and 2 three days to the power
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to buy three divide by Pirates Department by three.
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So these are dancers. Thank you.