All negative numbers are to the left of 0, that is, negative numbers are less than 0 and positive numbers are greater than 0. Negative numbers are smaller than positive numbers.

The two circular surfaces of the cylinder are called the bottom surface; The surrounding surface is called the side surface; The distance between two bottom surfaces is called height.

The surface area of the cylinder = the side area of the cylinder+the areas of the two bottom surfaces.

Transverse area of cylinder = bottom circumference × height.

Volume of cylinder = bottom area × height V=SH

V=πr？ ×H

V cone = V cylinder ÷3 = SH÷3

Two expressions with equal ratios like this are called proportions.

The four numbers that make up a proportion are called proportional terms. The two terms at both ends are called external terms of proportion, and the two terms in the middle are called internal terms of proportion.

According to the basic nature of proportion, if any three items in the proportion are known, another unknown item in this proportion can be found. Finding the unknown term in the proportion is called the solution ratio.

For example, because the bottom area of the cup is fixed, the volume of water varies with the height. The height of water increases, so does its volume, and the height of water decreases, so does its volume. The ratio of water volume to height is certain. )

In this way, two related quantities, one changes and the other changes. If the ratio of the corresponding two numbers in these two quantities is certain, these two quantities are called proportional quantities, and their relationship is called proportional relationship.

In the example 1, volume and height are proportional quantities.

Examples of reasons for the inverse ratio: (Because the volume of water is constant, the height of water changes with the change of bottom area. The bottom area increases, the height decreases, the bottom area decreases, the height increases, and the product of the height and the bottom area is certain. )

In this way, two related quantities, one quantity changes and the other quantity changes. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship.

In Example 3, the height is inversely proportional to the bottom area.

Positive proportion formula: Y÷x=k (certain) Inverse proportion formula: x×y=k (certain)

Origin of scale: When drawing a plan such as a map, it is necessary to reduce (or enlarge) the actual distance according to a certain proportion before drawing it on the drawing. At this time, it is necessary to determine the ratio of the distance on the map to the corresponding actual distance.

The ratio of the distance on a picture to the actual distance is called the scale of this picture.

Distance on the map: actual distance = scale

1 km = 100000 cm