Question 1: Solved

Find the lateral(side) surface area of the cone generated by revolving the line segment y = x/2, 0<= x <= 4, about the x-axis.

i got (pi*sqrt5)/2 just like the image however the answer is 4pi*sqrt5

now when i looked at the image they multiply my answer with

x^2/2

my question is how did they get that and why did they multiply it into the answer...

Question 2: how do i get

$\displaystyle x = y^4/4 + 1/8y^2$

in terms of y =

and find the derivative of it