Mathematical problems in the sixth grade of primary school

1. The two conical containers A and B have the same shape and the same volume. Containers a and b are inverted. The water in container A is 1/3 of the cone height, and the water in container B is 2/3 of the cone height. Which container has more water? How many times more is less?

Solution:

Conical containers A and B have the same shape and the same volume.

The bottom area of a cone is s, the height is h, the volume is v, and the bottom radius is R.

V=( 1/3)×S×H

The relationship between the radius r and the height of the bottom surface of the conical container is as follows:

R/R = H/H R, where h is the radius and height of the water surface when there is water.

The height of water in container A (H 1) is 1/3 of the cone height H.

R/r 1=H/(H/3) r 1=R/3

At this time, the horizontal plane area s 1 = π r = π r/9.

The volume v1= (1/3) × s1× h1= s/27.

The height H2 of water in container B is 2/3 of the cone height H.

R/r2=H/(2H/3) r2=2R/3

At this time, the horizontal plane area S2 = π (R2) = 4π r/9.

Volume V2=( 1/3)×S2×H2=8S/27.

At this time, there is more water in container B, which is 8 times that of container A. 。

2. Judge right or wrong.

1. If ab-5= 120, A and B are inversely proportional. (right)

2. A job is completed in 3 hours by Party A and 4 hours by Party B, and the efficiency ratio between Party A and Party B is 3: 4 (wrong).

3. In the sixth grade, 20% of the students participated in the photography group, which is equivalent to 25% of the students who participated in the painting group. Suppose there are 25 people in the photography group, how many people will participate in the drawing group? (there are two ways to understand).

Formula: 25×20%=5 (person)

5/25%=20 (person)

A: There are 20 people participating in the lottery team.

Equation: Solution: Suppose there are X people in the picture group.

25%x=25×20%

x=5/25%

x=20

A: There are 20 people participating in the lottery team.

4. If A: B = 5: 2 and B: C = 4: 3, then A:B:C=( 10):(4):(3).