Science:Math Exam Resources/Courses/MATH105/April 2014/Question 01 (b)

MATH105 April 2014

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Question 01 (b)
The volume of a right circular cone of radius $x$ and height $y$ is $V(x,y)={\frac {\pi x^{2}y}{3}}$. Graph the level curve $V(x,y)=\pi .$

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Calculate the level curve by setting $V(x,y)={\frac {\pi x^{2}y}{3}}=\pi$ and simplify the equation.

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Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Setting $V=\pi$, ${\begin{aligned}{\frac {\pi x^{2}y}{3}}&=\pi \\x^{2}y&=3\\y&={\frac {3}{x^{2}}}\\\end{aligned}}$ We plot the equation $y={\frac {3}{x^{2}}}$ noting that $x\geq 0$ is necessary for the curve to make physical sense.

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