Science:Math Exam Resources/Courses/MATH101/April 2017/Question 07 (b)

MATH101 April 2017
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Question 07 (b)

Let $R$ be the region to the right of the $y$ -axis and to the left of the curve $x^{2}={\sqrt {4+y}}$ with $y$ between $-4$ and $0$ . A reservoir dug into the ground has the shape that results from the region $R$ being rotated around the $y$ -axis.

(b) The reservoir from part (a) is filled with a fluid of density $1234{\text{kg}}/{\text{m}}^{3}$ . Find the work, in joules, required to pump the fluid out of the top of the reservoir. Use $g=9.8{\text{m}}/{\text{s}}^{2}$ for the acceleration due to gravity. A calculator-ready answer is sufficient.

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