It is known that there is an inscribed cube in the hemisphere. The ratio of the volume of the hemisphere to the volume of the cube is calculated It is known that there is an inscribed cube in the hemisphere, and the ratio of the volume of the hemisphere to that of the cube is calculated

It is known that there is an inscribed cube in the hemisphere. The ratio of the volume of the hemisphere to the volume of the cube is calculated It is known that there is an inscribed cube in the hemisphere, and the ratio of the volume of the hemisphere to that of the cube is calculated

Fill the hemisphere into a ball, and the cube will be folded into a cuboid
Let the radius of the ball be r and the side length of the cube be d
R^2=(d/√2)^2+d^2,d=√6R/3.
The ratio of the volume of hemisphere to the surface area of cube = (1 / 2) * (4 pie R ^ 3 / 3): 6D ^ 2 = pie R / 6

The distance between the two places is 210 kilometers. A passenger train and a freight train leave from the two places at the same time. They meet in 3.5 hours. The passenger train runs 28 kilometers per hour. How many kilometers does the freight train run per hour?

Suppose that the freight car travels x kilometers per hour, 3.5 × 28 + 3.5x = 210, & nbsp; 98 + 3.5x-98 = 210-98, & nbsp; & nbsp; 3.5x △ 3.5 = 112 △ 3.5, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 32, a: the freight car travels 32 kilometers per hour

Unit 2 of summer vacation life in Grade 6

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As shown in the figure, draw a circle through the four corners of a square with a circumference of 32 cm to find the area of the circle? I'm a primary school student,

A:
If the perimeter of a square is 32 cm, the side length is 32 △ 4 = 8 cm
Then the diagonal of the square is the diameter of the circle
Diagonal length = 8 ×√ 2 = 2R
So: the radius of the circle r = 4 √ 2cm
So: Area s = π R & # 178; = 32 π cm2
So: the area of this circle is 32 π square centimeter

If there are rational numbers a and B satisfying a = 2 and B = 1, find the value of AB / 1 + (a + 1) (B + 1) / 1 + (a + 2) (B + 2) / 1 ',' + (a + 2007) (B + 2007) / 1

Because 1 / [(a + n) (B + n)] = (a-b) [1 / (B + n)] - [1 / (a + n)] = 1 / (B + n)] - [1 / (a + n)], (n = 0,1,2,3,...), the original formula = [1 + (1 / 2) + (1 / 3) +... + (1 / 2007) + (1 / 2008)] - [(1 / 2) + (1 / 3) + (1 / 4) +... + (1 / 2008) + (1 / 2009)] = 1 - (1 / 2009) = 2008 / 2009

Four logs with a diameter of 10 cm are tied into a bundle with ropes. How many methods do you have? Are the ropes the same length? Explain the reason by calculation

There are two types. The first type is made into four bundles, the rope length is 10 * 3.14 + 10 * 6 = 31.4 + 60 = 91.4cm. The second type is made of two layers, two for each layer: 10 * 3.14 + 10 * 4 = 31.4 / + 40 = 71.4cm

If the side length of a is increased by 3 cm, the area will be increased by 39 square centimeters

　　（X+3)2-X2=39 X=5

The cycle of a planet circling the sun is 288 years. The earth and its orbit are seen as a circle. How many times is the distance between the sun and the planet?

This problem should be solved by Kepler's third law. The cube of the planetary revolution period is proportional to the square of the half major diameter of the orbit. For a celestial body moving in a circular orbit, the half major diameter can be simply replaced by a radius. There is the following relationship (TE / TX) ^ 3 = (RE / Rx) ^ 2T refers to the period, R refers to the radius of the orbit, e refers to

Test paper of the first lesson of physics in the second grade of the people's Education Press
I want the first one

&#(2009-8226; Jinzhou City) 2009 Spring Festival Gala sketch "not bad money" won the favor of the national audience. Xiao Yan heard that the voice of "Xiao Shenyang" was produced by and spread by, and the voice of "Xiao Shenyang" imitated "Dao Lang" very lifelike because of their similarity
&#At the opening ceremony of the Beijing Olympic Games, the magnificent "song of beating fou" was produced by the surface of the fou, and then spread to the audience's ears. The spectacular scene was transmitted to all parts of the country by synchronous communication satellite through waves
 (09 Yantai). The principle that some deaf patients can hear sound with bone conduction hearing aids is that__________________________________ .
&#It is pointed out that the sound is mainly transmitted by: (1) when the ear is close to the pillow, you can hear the "tick" sound of the mechanical watch under the pillow, which is transmitted by; (2) when the diver hears the conversation of the people on the shore underwater, it is transmitted by
 (Jilin, 2004)
&#In the self-study class of Chaoyang City, naughty Xiao Ming sings in the classroom corridor. He touches his throat and feels his throat in the classroom________ All the students in the classroom heard the song, which indicated that the sound could pass through__________ Xiao Juan, who is meditating, covers her ears with her hands. She thinks Xiao Ming's singing is a good song__________ (insert "music" or "noise")
 6. [2009 &; Tianjin] erhu is a stringed instrument invented by the working people in China. Before playing, actors often need to adjust the tightness of the strings in order to adjust the []
 A. loudness B. pitch
 C. timbre D. amplitude
&#"Dare not speak aloud, afraid to frighten the people in the sky." here "high" refers to the voice_______ (fill in "tone", "loudness" or "timbre") big. Chang'e in the Moon Palace won't hear your voice, because________ "Chang'e-1" satellite in orbit around the moon to the ground to send back the last voice: "after a year of space travel, my mission has ended,..." This voice is through____________ It's coming back to earth
 8. [2009 &; Jiangsu Province] as shown in Figure 1, when a hanging ping-pong ball touches a tuning fork that is making a sound, the ping-pong ball will bounce away many times
 A. can sound propagate in vacuum
 B. causes of sound
 C. is pitch related to frequency
 D. does sound transmission take time
 9. [2009 &; Yichang City] when boys and girls sing in chorus, the baritone is loud and the soprano is low, so the loudness is high and the tone is high
 (09 Loudi, Hunan). Noise monitoring equipment is installed at the main road crossing in Loudi City. At a certain time, the display screen of the equipment shows 49.20, the unit of which is
 10 [2009 &; Changsha] a student from a physics interest group designed an experimental device as shown in Figure 3. When a glass bottle filled with water is squeezed with force, the water surface in the thin glass tube rises obviously. This is figure 3, which uses the change of water surface in the thin glass tube to magnify the tiny deformation of the glass bottle
 A. place the tuning fork close to the table tennis ball, and the table tennis ball is bounced away to show that the tuning fork is vibrating
 B. in exploring the current in resistance and its two ends
 voltage relationship, keep the resistance unchanged to study
 relationship between current and voltage
 C
 to make research more convenient, we usually use a
 resistance to replace multiple resistors
 D. the magnetic field of a magnet is described by magnetic induction lines
 27. In the 100 meter race, the timekeeper counts the time only after hearing the sound of the starting gun. The result he recorded is 13.69s. What is the real result of the athlete? (the temperature was 15 ℃)

If the height and length of the hypotenuse of a right triangle are 4.8cm and 10cm respectively, what is the circumference of the right triangle?
Pro, it's better not to have too many symbols

Let the two right sides of the right triangle be X1 and X2 respectively
Then we know that the perimeter is X1 + x2 + 10
We can know that X1 * x2 = 1.8 * 10 if we have the solution of triangle area
From Pythagorean theorem, we know that the square of X1 + the square of x2 = 10 and the square of x2 = 100
So X1 + x2 = 14
The perimeter is 14 + 10 = 24cm