Question

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

Answer 1

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

Answer 2

so i used similar triangles and obtained h=20-2r

..

the model answers showed that they used pythagoras..

why is my methods incorrect?

Answer 3

height is based off a curve, not a line

Answer 4

height = sqrt(10^2 - x^2)

Answer 5

oh, and even tho thats pythagorean, its really based off of the equation for the circle of the sphere

Answer 6

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?

Answer 7

all points equidistant from the center ... in this case the origin ... is the equation

x^2 + y^2 = r^2

Answer 8

height is measured as 2y in this case. radius is x

Answer 9

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?

Answer 10

repeating faulty arguments do not make them any more correct ...