Additive space in the lower part with tcolorbox

Question

Using the tcolorbox package to produce exercises for a textbook, I use the option invisible to let space for students for writing their solutions. In practice, the students need more space to write the solution than take the solution written. So how can I add a vertical space, say 20mm, for the option invisible? More, how can I play on this space, so add 10mm in the invisible part for short exercises, and 20mm for long ones ?

I give the program used:

\documentclass{book}

\usepackage{etoolbox}
\usepackage[most]{tcolorbox}

\NewTColorBox[auto counter,number within=chapter]{exercise}{m+O{}}{%
    enhanced,
    breakable,
    colframe=green!20!black,
    colback=yellow!10!white,
    coltitle=green!40!black,
    fonttitle=\bfseries,
    underlay={\begin{tcbclipinterior}
        \shade[inner color=green!80!yellow,outer color=yellow!10!white]
            (interior.north west) circle (2cm);
        \draw[help lines,step=5mm,yellow!80!black,shift={(interior.north west)}]
            (interior.south west) grid (interior.north east);
        \end{tcbclipinterior}},
    title={Exercise~ \thetcbcounter:},
    label={exercise:#1},
    attach title to upper=\quad,
    segmentation style={double=white,draw=green!20!black,double distance=1pt,solid},
    lowerbox=invisible,
    savelowerto=solutions/exercise-\thetcbcounter.tex,
    record={\string\solution{#1}{solutions/exercise-\thetcbcounter.tex}},
    #2
}

\begin{document}
\pagestyle{empty}
\tcbstartrecording
\begin{exercise}{Ex1}[coltitle=cyan!80!black]
Compute the derivative of the following function:
\begin{equation*}
f(x)=\sin((\sin x)^2)
\end{equation*}
\tcblower
The derivative is:
\[f^\prime(x) = \cos((\sin x)^2) 2\sin x \cos x.\]
\end{exercise}

\tcbstoprecording
\end{document}

Answer 1

Not sure about this answer, but you can always fix a certain height for the whole box or add to natural height some space. This space is divided between top and lower parts but you decide how. If all should go to lower part, use space to lower option. More information in section 4.10 Height control.

\documentclass{book}

\usepackage{etoolbox}
\usepackage[most]{tcolorbox}

\NewTColorBox[auto counter,number within=chapter]{exercise}{m+O{}}{%
    enhanced,
    breakable,
    colframe=green!20!black,
    colback=yellow!10!white,
    coltitle=green!40!black,
    fonttitle=\bfseries,
    underlay={\begin{tcbclipinterior}
        \shade[inner color=green!80!yellow,outer color=yellow!10!white]
            (interior.north west) circle (2cm);
        \draw[help lines,step=5mm,yellow!80!black,shift={(interior.north west)}]
            (interior.south west) grid (interior.north east);
        \end{tcbclipinterior}},
    title={Exercise~ \thetcbcounter:},
    label={exercise:#1},
    attach title to upper=\quad,
    segmentation style={double=white,draw=green!20!black,double distance=1pt,solid},
    lowerbox=invisible,
    savelowerto=solutions/exercise-\thetcbcounter.tex,
    record={\string\solution{#1}{solutions/exercise-\thetcbcounter.tex}},
    #2
}

\begin{document}
\pagestyle{empty}
\tcbstartrecording
\begin{exercise}{Ex1}[coltitle=cyan!80!black]
Compute the derivative of the following function:
\begin{equation*}
f(x)=\sin((\sin x)^2)
\end{equation*}
\tcblower
The derivative is:
\[f^\prime(x) = \cos((\sin x)^2) 2\sin x \cos x.\]
\end{exercise}

\begin{exercise}{Ex2}[coltitle=cyan!80!black, add to natural height=2cm, space to lower]
Compute the derivative of the following function:
\begin{equation*}
f(x)=\sin((\sin x)^2)
\end{equation*}
\tcblower
The derivative is:
\[f^\prime(x) = \cos((\sin x)^2) 2\sin x \cos x.\]
\end{exercise}

\tcbstoprecording
\end{document}