Skip to main content\(\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Instructions.
Use the slider
\(k\) at the top left to change the linear scale factor of the blue image cone. Notice how changing the linear scale factor affects both the radius (
\(r'\)) and the height (
\(h'\)) simultaneously.
Observe the dynamically calculated volumes on the left side of the board. As you adjust the slider, verify that the Volume Scale Factor is always exactly equal to the cube of the linear scale factor (
\(k^3\)).