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Vectors and matrices — Question 19

QCAA 2020, Paper 1 · 7 marks

Q19 · 2020 · Technology-freeComplex unfamiliar7 marks

QUESTION 19 (7 marks)

A circular-based bowl has been positioned symmetrically on a Cartesian plane as shown in the diagram. The bowl has a shape that can be generated by rotating the curve y=48−x−1y=\dfrac{4}{8-x}-1 about the yy-axis for 4≤x≤7.64\le x\le7.6 cm. The bowl is being filled with a liquid at the rate of 7π7\pi cm3^3 s−1^{-1}. Determine the rate at which the depth of liquid is increasing when the depth of liquid reaches one-third of the height of the bowl.
Cross-section of the circular-based bowl on Cartesian axes
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