marigirl
  • marigirl
can you please check over why my method is incorrect for this question. Topic differentiation A Cylinder of height h and radius r is inside a sphere of of radius 10. find the value of r that will maximise volume of cylinder
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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marigirl
  • marigirl
Volume of a cylinder is v=pi r^2*h so i went about getting an expression or h to substitute in by using similar triangles
marigirl
  • marigirl
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marigirl
  • marigirl
so i used similar triangles and obtained h=20-2r .. the model answers showed that they used pythagoras.. why is my methods incorrect?

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amistre64
  • amistre64
height is based off a curve, not a line
amistre64
  • amistre64
height = sqrt(10^2 - x^2)
amistre64
  • amistre64
oh, and even tho thats pythagorean, its really based off of the equation for the circle of the sphere
marigirl
  • marigirl
but if u take the into consideration the height and radius measurements from the origin of x and y axis - wont it be a straight line?
amistre64
  • amistre64
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amistre64
  • amistre64
all points equidistant from the center ... in this case the origin ... is the equation x^2 + y^2 = r^2
amistre64
  • amistre64
height is measured as 2y in this case. radius is x
marigirl
  • marigirl
but if u take the into consideration the height and radius measurements from the origin of x and y axis - wont it be a straight line?
amistre64
  • amistre64
repeating faulty arguments do not make them any more correct ...
Loser66
  • Loser66
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Loser66
  • Loser66
where r is the radius of the cylinder, h is the height of it
marigirl
  • marigirl
i am not trying sound smart .. i was just generally thinking about these problems... i did a problem before with a cylinder inside a triangle..
amistre64
  • amistre64
a sphere is not a triangle :)
amistre64
  • amistre64
a cone would have a linear setup ... since its profile is a triangle
marigirl
  • marigirl
in that case- similar triangle works.. but u cant apply the height is based off a curve...I am sorry i didnt mean to sound arrogant.. im just thinking
amistre64
  • amistre64
thinking is good ... just some thoughts are worse than others
marigirl
  • marigirl
I appreciate your answer. thank you
amistre64
  • amistre64
x^2 + y^2 = 10^2 is the equation of your circle, which your cylindar sets in y = sqrt(100-x^2) is the top of the sphere, which is 1/2 the height of the cylindar from the x axis
marigirl
  • marigirl
yes i get how that formula is used here. so i guess it really comes down to what the cylinder is inscribed inside...if it is a sphere then its properties would be different to a cone. Thank you
amistre64
  • amistre64
V = pi r^2 h, r=x, and h=2sqrt(100-x^2) V' = pi (2r r' + r^2 h') V' = 0 when, 2r r' + r^2 h' = 0 just some of my thoughts is all
amistre64
  • amistre64
correct, good luck :)
marigirl
  • marigirl
thank you!

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