Solve the Problem $\mathrm { y } = 5 \mathrm { x } ^ { 2 } , 0 \leq \mathrm { x } \leq 2$

question 183

Multiple Choice

Solve the problem.
-A tank is designed by revolving the parabola $\mathrm { y } = 5 \mathrm { x } ^ { 2 } , 0 \leq \mathrm { x } \leq 2$ , about the $\mathrm { y }$ -axis. The tank, with dimensions in meters, is filled with water weighing $9800 \mathrm {~N} / \mathrm { m } ^ { 3 }$ . How much work will it take to empty the tank by pumping the water to the tank's top? Give your answer to the nearest $\mathrm { J }$ .

• A) 256,563 J
• B) 8,210,029 J
• C) 1,642,006 J
• D) 24,630,086 J

---

Definitions:

Negative Feedback

A regulatory mechanism in which a stimulus causes an opposite output in order to maintain an optimal level of whatever is being regulated.

Density Dependent

Factors whose effects on the size or growth of the population vary with the population density.

Fecundity

The potential capacity of an individual to produce offspring.

Offspring

Biological children or descendants of parents, encompassing both singular and plural progeny.