A Water Tank Is Formed by Revolving the Curve $y = 2 x ^ { 4 }$

question 43

Multiple Choice

A water tank is formed by revolving the curve $y = 2 x ^ { 4 }$ about the $y$ -axis. Find the volume of water in the tank as a function of the water depth, $y$ .

• A) \(V ( y ) = \frac { \pi } { 2 \sqrt { 2 } } y ^ { 1 / 2 }\)
• B) \(V ( y ) = \frac { 3 \pi } { 2 \sqrt { 2 } } y ^ { 3 / 2 }\)
• C) \(V ( y ) = \frac { \pi } { 9 } y ^ { 9 }\)
• D) \(V ( y ) = \frac { 2 \pi } { 3 \sqrt { 2 } } y ^ { 3 / 2 }\)

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Definitions:

BCR

Benefit-Cost Ratio, a numerical expression comparing the benefits of an action or project to its costs.

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A measure of how effectively resources (money, time, effort) are used to achieve a desired outcome or goal.

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