\documentclass[letterpaper,12pt]{article}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath}
\usepackage[letterpaper,margin=1in,includehead=true]{geometry}
\usepackage{comment}
\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{enumerate}
\pagestyle{fancy}
\usepackage{color}
\usepackage{wrapfig}
%\usepackage{enumitem}
\usepackage{tikz, tikz-3dplot, pgfplots}
\usetikzlibrary{calc}
\pgfplotsset{compat=newest}



\title{\vspace*{-1.5in}\textbf{Math 2300-007: Quiz 4b}}
\date{}
\author{}


\begin{document}
\maketitle
%\underline{Math 1300-400: Quiz 1}
\lhead{Math 2300-007: Calculus II}
\rhead{Feb. 9, 2018}
\chead{Quiz 4b}
\vspace{-.5in}
\noindent
{Name: \underline{\phantom{Aalsdkjflaskdjflaskjflksdjflkdsjf}}} \hfill{Score: \underline{\phantom{lksdjflkdsjf}}}\\[3pt]

\begin{enumerate}
\item(1 point) In a sentence or two, what would you say is the main \textbf{difference} between the shell method and the washer/disk method for finding the volume of a solid of revolution? \vskip1in
\item(4 points) Suppose you are asked to use the \textbf{shell method} to calculate the volume of the solid formed by rotating around the $y$-axis the region bounded by the curves $y=\sqrt{x}$, $y=0$, $x=2$, and $x=6$. %Cross-sections are disks like the one shown to the right. Fill the blanks with expressions involving $x$.
\begin{enumerate}[(a)]
\item Would your integral be with respect to $dx$ or $dy$?\vskip1cm
\item On the graph below, draw a small rectangle that is consistent with your answer from part (a).
\item Next to the graph, sketch the cross-section (small slice) that you get from rotating your rectangle around the $y$-axis.

\begin{center}
\begin{minipage}{.5\textwidth}
\begin{tikzpicture}
\begin{axis}[axis lines = center,enlargelimits, 
%xtick={-5,-4,...,5},
%ytick={-5,-4,...,5},
xlabel={$x$},
ylabel={$y$},
xlabel style={below right},
ylabel style={above left},
%xmax=10
]
\addplot[fill= gray!40, smooth, domain = 1.412:2.4495]({x^2},{x})--(axis cs: 6,0)--(axis cs: 2,0)--cycle;
%\plot 2.1213:2.236]({x^2},{x})(axis cs: 4,2.236)--(axis cs: 5,2.236)--(axis cs: 5,0)--(axis cs: 4.5,0)--cycle;
%\addplot[fill=gray!90, domain=4.6:5]({x},{2.236})--(axis cs: 5,0)--(axis cs: 4.6,0)--cycle;
%\addplot {(axis cs: 4.5,2.236)--(axis cs: 5,2.236)--(axis cs: 5,0)--(axis cs: 4.5,0)--cycle;
\addplot[smooth, domain = 0:3]({x^2},{x});
%\addplot ellipse (axis cs: 8,0) ellipse (1 and 2);
\addplot[->,smooth, domain = 110:390]({.5*cos(x)+ 0},{.1*sin(x)+2.5});
\end{axis}
\draw (7.2,5.3) node{$y = \sqrt{x}$};
%\draw[|-|] (3.48,.2)--(3.76,.2);
%\draw (3.62,-.2)node{$dx$};
%\draw[fill=gray] (11,0.5) ellipse (.6 and 4);
%\draw[color = gray, fill = gray] (11,4.5)--(11.3,4.5)--(11, 4.3)--cycle;
%\draw(11,4.5)--(11.3,4.5);
%\draw[color = gray, fill = gray] (11,-3.5)--(11.3,-3.5)--(11,-3.3)--cycle;
%\draw(11,-3.5)--(11.3,-3.5);
%\draw[fill = white] (11.3,0.5) ellipse (.6 and 4);
%\draw[fill = gray!40] (11.3,0.5) ellipse (.6 and 4);
%\draw[fill=black] (11.3,0.5) ellipse (.75pt and 1.5pt);
%\draw (11.3,0.5)--(11.3,2) node[draw = black, fill = white, inner sep = 1pt, right]{$r = \underline{\phantom{alsdkfjasdf}}$}--(11.3,4.5); 
%\draw (11.3,0.5)--(11.3,2) node[right]{$r$}--(11.3,4.5);
%\draw[|-|] (11,4.7)--(11.3,4.7);
%\draw (11.15,5)node{$w$};
\end{tikzpicture}
\end{minipage}
\qquad
\framebox{\begin{minipage}{2in}

\begin{flushleft}
Cross-section (small slice):
\end{flushleft}
\hspace{1.9in}
\vspace{1.7in}
\end{minipage}}
\end{center}

\item What is the volume of the cross-section (small slice) that you drew?\\[6pt]

$V_{\text{slice}} ={\underline{\phantom{an answer an answer}}}$
\end{enumerate}


\end{enumerate}

\pagenumbering{gobble}

\end{document}
