Question

a circle is cut in a pack-men shape such that the radius of the sector is x,find the largest possible volume of the cone that is formed from this circle,if the cone has height , h=2x+1

Answer 1

this problem seems to be inconsistent.
if x is the radius of the circle then it will correspond to the slant height of the cone
and you have x^2 = h^2 + r^2 (r the radius of the cone)
but h = 2x+1 and you have x^2 = (2x+1)^2 + r^2
or
x^2 = 4x^2 + 4x +1 +r^2

that says the hypotenuse is smaller than one of the sides.... not good.

Answer 2

i made this munbers by my self ,this problem is my original thought i understand the error but hw can we avoid it how can i change the height

Answer 3

r=2x+1,h=x

Answer 4

okay i see the folly thanks guys