(1) cuboid volume v = ABC

(2) the volume of the cube v = a3

(3) The volume of the cylinder V = SH = π R2, and S is the area of the bottom of the cylinder.

(4) The volume of the cone v = 1/3sh = 1/3π r2h, and s is the area of the bottom of the cone.

2. The core idea:

Master the thinking method of transformation. The so-called transformation mainly refers to transforming a certain figure into a standard rectangle, square, circle or other regular figures, so as to calculate their perimeters.

Example 1: A regular cube with a side length of 8 consists of several regular cubes with a side length of 1. Now, the surface of the big cube should be painted with color. How many small cubes have you drawn? ( )

A.296b.324c.328d.384 (2004 Central A-level title)

Analysis: This problem seems to have nothing to do with volume, but it can be transformed into a typical volume problem. To know how many cubes are dyed, just ask how many cubes are not dyed. The total number of cubes should be the volume of cubes, that is, 6.3 = 5 12, while the uncolored volume (number of small cubes) is 216, so the number of colored small solids is 5 12-2 16 = 296.

So, choose an answer.

Ex. 2: In a cold drink shop, soda used to be packed in cylindrical paper cups, and each cup sold for 2 yuan money, which sold 100 cups a day. Now we use conical paper cups with the same bottom area and height, and each cup costs only 1 yuan. If the total amount of soda sold in this store remains the same every day, what is the daily sales now? ( )

A.50% B.100% C.150% D.200% (2003 Central Class B real question)

Analysis: Past sales = 2×100 = 200; Now change it to a conical paper cup. According to the volume formula, the volume of a cylinder with equal base and equal height is three times that of a cone. So now the daily sales =1×100 ÷1/3 = 300. Obviously, the sales in the past were 300 ÷ 200 = 150%.

So, the answer is C.