anonymous one year ago ques

1. anonymous

cross sectional area of a hollow cylinder of inner radius $x$ of thickness $dx$ will be $2\pi xdx??$ My attempt: |dw:1442644796376:dw| If we open this we get a trapezium if I'm not wrong |dw:1442644914454:dw| 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 $dA=2\pi x dx$

2. dan815

cross sectional area if u slice it how?

3. IrishBoy123

or $$dA = \pi (x + dx)^2 - \pi x^2 = 2 \pi x \, dx$$

4. anonymous

Oh I was intrigued with opening it, I forgot about the area formula, either way the term containing (dx)^2 is ignored right

5. IrishBoy123

and it's brill they agree!!

6. anonymous

lol, math always agrees!!

7. anonymous

cheers

8. IrishBoy123

the dx^2 disappearing is the ghost of departed quantities https://en.wikipedia.org/wiki/The_Analyst