1: Make a single-layer hat with a piece of cloth. The top of the hat is a cylinder, and the brim is a ring. It is known that the radius, height and brim width of the top are all 1 decimeter. If you can't remember the seams, how many square decimetres of cloth do you need to make this hat?

The area of the hat top is

/kloc-0 /×/kloc-0 /× 3.14 = 3.14 (square decimeter)

The side area of the hat is

1× 2× 3.14×1= 6.28 (square decimeter)

The outer radius of the edge is

1+ 1 = 2 (decimeter)

The area of the edge is

2× 2× 3.14-/kloc-0 /×/kloc-0 /× 3.14 = 9.42 (square decimeter)

Make this top hat with at least cloth.

3.14+6.28+9.42 =18.84 (square decimeter)

2; If a=c(a, b, c is not zero), if (c) is certain, (a) and (b) are directly proportional, and if (a) is certain, (b) and (c) are inversely proportional.

3. The fractional value is certain, is the numerator directly proportional to the denominator?

because

Molecule: denominator = fractional value (certain)

therefore

The fractional value is constant, and the numerator is proportional to the denominator.

4. If A=6B, then must A and B be inversely proportional?

A=6B

A: B =6

therefore

If A=6B, then a and b must be proportional.

5. The volume of cylindrical bucket is 75.36 cubic decimeter. The diameter of the inner bottom surface is 4 decimeters, and it is filled with 3/4 water. How high is the water?

The volume of water is

75.36× 3/4 = 56.52 (cubic decimeter)

The bottom area of the bucket is

(4 ÷ 2) × (4 ÷ 2 )× 3.14 =12.56 (square decimeter)

Water level height

56.52 ÷ 12.56 = 4.5 (decimeter)