# Thread:

1. ## Find the volume of the solid

Find the volume of the solid whose base is the region between the curve $y=x^3$ and y-axis from $y=0$ to $y=1$, and whose cross sections taken perpendicular to the y-axis are squares.

I don't understand "whose cross sections taken perpendicular to y-axis are squares".

How can I solve this problem? If possible, would you please explain step by step?

Thank you very much.

2. Picture a bunch of squares stacked up perp.to the y-axis in your given region.

This is NOT a volume of revolution. Since we are perp to the y-axis we will integrate wrt y.

$x=y^{\frac{1}{3}}$

The area of a square is $x^{2}$

So, we have $\int_{0}^{1}y^{\frac{2}{3}}dy$
{"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": 6, "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": 0.9069352746009827, "perplexity_flag": "middle"}