Question

ques

Answer 1

cross sectional area of a hollow cylinder of inner radius \[x\] of thickness \[dx\]
will be
\[2\pi xdx??\]
My attempt:

If we open this we get a trapezium if I'm not wrong

Then we apply area of trapezium formula
\[A=\frac{a+b}{2}.h\]\[\therefore dA=\frac{2\pi(x+dx)+2\pi x}2{}.dx\]\[\therefore dA=(\pi(x+dx)+\pi x)dx\]\[dA=(\pi x+\pi dx+\pi x)dx\]\[dA=(2\pi x+\pi dx)dx=2\pi x dx+\pi(dx)^2\]
Since dx is extremely small, (dx)^2 will be even smaller and can be ignored
\[dA=2\pi x dx\]