Question

You are in charge of the evacuation and repair of the storage tank shown here. The tank is a hemisphere of radius 10 ft and is full of benzene
weighing 56 lb / ft . A firm you contacted says it can empty the tank for ½ cent
per foot-pound of work. Find the work required to empty the tank by pumping the benzene to an outlet 2 ft above the top of the tank. If you have $5000 budgeted for the job, can you afford to hire the firm?

Answer 1

Calculate the volume to get the amount of benzene stored in the tank and multiply by the weight parameter given to calculate the weight and then once weight is known, multiply the cost with the weight obtained

Answer 2

@heybhai i dont understand what youre saying

Answer 3

@professional_loser_ I can solve it but the moderator has issued a warning against me, so i just gave u hint to tackle it. Ask moderator if he allows me to solve the problem numerically.

Answer 4

@heybhai i understand the hint, the problem is i need to find the amount of work needed to move the benzene first not how much benzene is in the tank.

Answer 5

@professional_loser_ Once u have weight of benzene( vol*56) multiply with 9.8 to get Weight,F now to calculate work use W=f*d
where d=2 the distance it need to be lifted

Answer 6

why 9.8?

Answer 7

That's the acceleration due to gravity of Earth.Its fixed.

Answer 8

how would you solve it using integrals?

Answer 9

\[\int\limits_{a}^{b} F(x) dx\], where F(x) is the force

Answer 10

would i use 0 and 10 or 0 and 12 as the limits?

Answer 11

I guess it will be 0 to 12 as the tap is 2 cm above tank.

Answer 12

thanks

Answer 13

Welcome @professional_loser_