# Percentage ratio of areas

I don't understand a question from a Math exercise. I did many things asked before, but I found this part very difficult to understand:

What is the percentage ratio between the combined area of six cylinder bottoms and the area of box bottom in case A?

I just calculated the area of the box (which is a rectangle): 66*396 = 26136. And about the cylinders, we know that h=187 mm and r=33 mm...

Maybe is a problem of my bad English, but I can't answer to the above question. Could you bring me some light?

Thank you very much in advance!

-

## 1 Answer

The cylinders seem to have a circular cross section of radius 33 mm, so the area of the bottom of one is $\pi (33\ \mathrm{mm})^2$. Six will just fit in a row in a rectangle $66\ \mathrm{mm} \times 396\ \mathrm{mm}$, whose area you have calculated. So it is $\frac{6 \pi 33^2}{66\times396}$ which should be the same as the ratio between a circle and the circumscribed square (why?).

-

@Rahul Narain:  Thanks. – Ross Millikan Dec 28 '11 at 4:32
{"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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "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": 0.9633264541625977, "perplexity_flag": "middle"}