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\LARGE 

{\hspace{50mm}Quiz 5
\hspace{50mm}Name:\hspace{20mm}}


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Directions:  Answer each question to the best of your ability.  You may use a calculator, but you must show all work to receive full credit.  For problems 1 and 2, set up your definite integral based on the Riemann sum with the conditions given.  If it is helpful, draw a picture of the problem.  (5 pts each)
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\begin{enumerate}
\item Find the volume of the top half of a sphere with radius 10 taking vertical slices.  
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\item Find the area of a right triangle with height 15 and a hypotenuse of 30 taking EITHER horizontal or vertical slices. 
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\item Find the volume of revolution of $f(x)=\frac{4}{x}$ on [2,5] around the $x$-axis.
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\item Find the volume of revolution of the area between $f(x)=2x^2$ and $g(x)=\frac{1}{2}x^3$ on [0,4] around the $x$-axis.
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\item Find the volume of revolution of the area between $f(x)=2x^2$ and $g(x)=\frac{1}{2}x^3$ on [0,4] around the $y$-axis.
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