$215-$ Calculus II

Shiam

omework: Section $6\mathrm{.}7($day $2)$ Homework

Question

Part $4$ of $4$

Completed: $8$ of $12$ My score: $\frac{8}{12}$ pts $(66\mathrm{.}67\%)$

A water tank, shown in the figure, is shaped like an inverted cone with height $12$ m and base radius $1\mathrm{.}5$ m $.$

a$.$ If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Use $1000k\frac{g}{m^3}$ for the density of water and $9\mathrm{.}8\frac{m}{s^2}$ for the acceleration due to gravity.

b$.$ Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full? Explain.

B$.{\displaystyle \underset{0}{\overset{12}{}}}(1000(9\mathrm{.}8)(12-y)(\frac{y^2}{64}))dy$

The amount of work required is approximately $264600$ J$.$

$($Type an integer or a simplified fraction. Type an exact answer, using $$ as needed.$)$

b$.$ Select the correct choice and, if necessary, fill in the answer box to complete your choice.

A$.$ Yes. It takes exactly half as much work to pump all the water out of the tank when it is filled to half its depth.

B$.$ No$.$ The amount of work required to pump all the water out of the tank when it is filled to half its depth is approximately $($Type an integer or a simplified fraction. Type an exact answer, using $$ as needed.$)$

ne solve this

View an example JUST WANT PART B

Get more help