Imagine riding on a merry-go-round at the center. as you walk to the outer edge, the merry-go-round slows in order to conserve angular momentum. true or false?

True

Explanation:
When riding at the center, the angular momentum is
Iω²
where I = rotational inertia
ω = angular velocity.

When you move away from the center to a radius r, you add to the rotational inertia by mr², where m is your mass.
The new rotational inertia becomes I + mr².

If the new angular velocity is ω₁. then 
(I + mr²)ω₁² = Iω²
Therefore
ω₁² = Iω²/(I + mr²)

Therefore ω₁ < ω in order to conserve angular momentum.

work done in pumping the entire fuel is 1399761 J

Explanation:

weight per volume of the gasoline = 6600 N/m^3

diameter of the tank = 3 m

length of the tank = 6 m

The height of the tractor tank above the top of the tank = 5 m

The total volume of the fuel is gotten below

we know that the tank is cylindrical.

we assume that the fuel completely fills the tank.

therefore, the volume of a cylinder =  

where r = radius = diameter ÷ 2 = 3/2 = 1.5 m

volume of the cylinder = 3.142 x  x 6 = 42.417 m^3

we then proceed to find the total weight of the fuel in Newton

total weight = (weight per volume) x volume

total weight = 6600 x 42.417 = 279952.2 N

therefore,

the work done to pump the fuel through to the 5 m height = (total weight of the fuel) x (height through which the fuel is pumped)

work done in pumping = 279952.2 x 5 = 1399761 J