1. Solution: Suppose the radius of the base circle of the cylinder is R, then the height of the cylinder is 2R, and the edge length of the cube is 2R. There is an equation:

3.14×R2×2R =628

6.28×R3=628

R3=628÷6.28

R3=100

The volume of the cube is equal to: 2R× 2R×2R=8×R3=8×100=800 (cubic centimeters)

Answer: The volume of the cube is 800 cubic centimeters

2. The largest cylinder is on the cube. The surface is inscribed in the circle, so the diameter is 8, which means the radius is 4. The height is still the height of the cube.

So: 4^2*3.14*8=401.92

3, 3.14*16*16*30=24 115.2 cubic centimeters

4, oil The barrel filled with oil is 3.925*2=7.85 liters

And 1 liter=1 cubic decimeter=1000 cubic centimeters

So the volume of the oil barrel is 7.85*1000=7850 cubic centimeters

So the height of the oil barrel = volume/bottom area

When π is 3.14

Radius = 10cm

Bottom area = 3.14 *102=314 square centimeters

So height=7850/314=25 centimeters

5, 3.14*2r*2r*1/2h=40

3.14 *r*r*h=20

The original bucket can hold 20 kilograms of water