Science:Math Exam Resources/Courses/MATH110/December 2015/Question 08 (a)

MATH110 December 2015

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Question 08 (a)
If a spherical tank of radius 2 metres is filled up to h metres with water, then the volume of water $V$ in the tank is given by the following function: $V(h)=\pi h^{2}\left(2-{\frac {h}{3}}\right),$ where $h$ is measured from the deepest point in the tank. (a) What is the domain of the function $V(h)$ in this context?

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?

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Hint
What can be the upper and lower bound for the height of the water in a spherical tank?

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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. The lowest height of the water is when $h=0$, and the maximum height of the water is when $h=4$, i.e. the diameter of the sphere, so Domain: $\color {blue}\{h\in \mathbb {R} :0\leq h\leq 4\}$ .