A chemical company is designing a cylindrical storage tank with a fixed volume, $V$. The cost of the material used for the tank’s construction depends on its surface area. The tank has a circular base and top, and the curved side is made from a different material. Let $r$ be the radius of the circular base/top and $h$ be the height of the tank. The base and top cost $a$ dollars per unit area, while the curved side costs $b$ dollars per unit area.
b. Determine the value of $r$ that minimizes the cost $C$, expressing your answer in terms of $a$, $b$, and $V$. Justify that this value of $r$ yields a minimum cost by using calculus.
Marking your answer...
This may take a few seconds
Sign up for free to see your full marking breakdown and personalised study recommendations.
Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 5 marks, testing your understanding of Literal and General Equations. It falls under Algebra, number and structure in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers algebra of functions, inverse functions, and solutions of equations and systems of equations.
solution of literal equations and general solution of equations involving a single parameter
All free, all instant AI marking.
Solve the following equation for $x$ in terms of $a$, $b$, and $c$, assuming $a \neq 0$: $a(x - b) = c$
Consider the equation $\cos(kx) = a$, where $k$ and $a$ are real parameters with $k > 0$. Analyse the number of solutions for $x$ in the int…
Consider the equation $\sin(x) = k$, where $k$ is a real number and $x \in [0, 4\pi]$. Explain how the number of solutions for $x$ changes a…
StudyPulse has thousands of VCE Mathematical Methods questions with full AI feedback, mark breakdowns, progress tracking, and study notes across every Key Knowledge point including Literal and General Equations.
