# Thread:

1. ## find surface area of a donut

I have a problem where i dont even know where to begin. Usually, when i post problems here i have something to show but this time i dont. Im sorry for that.

here is the problem
:

FInd the surface area of the torus (or donut) obtained by rotating the circle (x - b)2 + y2 = a2; (a < b) about the
y-axis.

would i do something like the Area of a surface of revolution theorem?:

$S = 2 \pi \int_a^b f(t) \sqrt {(dx/dt)^2 + (dy/dt)^2} dt$

if so i am not even sure what to do to get it into the form to put it into that formula?

Any help is appreciated since i am lost!!

Thank you

2. ## Re: find surface area of a donut

Originally Posted by icelated
FInd the surface area of the torus (or donut) obtained by rotating the circle (x - b)2 + y2 = a2; (a < b) about the y-axis.
Use the First Guldin Theorem: the surface area $S$ of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of the arc length $s$ of the generating curve and the distance $d$ traveled by the curve's geometric centroid $\bar{x}$ .

3. ## Re: find surface area of a donut

Originally Posted by FernandoRevilla
Use the First Guldin Theorem:
Im not suppose to use pappus's theorem. When i googled First Guldin Theorem everything came back to pappus. What is First Guldin Theorem? =(
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8863521218299866, "perplexity_flag": "middle"}