Out of a cube, cuboid, cylinder and a sphere of same volume, which one will have minimum surface area?
Calculate it. A cube is a special case of a cuboid, so you can calculate only the more general case of the cuboid. [math]V_{\mathrm{cuboid}}=w l h[/math], [math]A[/math][math]_{\mathrm{cuboid}}=2(w l+l h+h w).[/math]Using the method of your choice, (e.g. Lagrange Multipliers), it is straightforward to show that the surface area is minimized subject to constrained volume when [math]w=l=h[/math], which reduces to the cube. In this case, for unit volume, the cube's area is 6.[math]V_{cylinder}=\pi r^2 h[/math], [math]A[/math][math]_{cylinder}=2\pi(r^2+r h)[/math].Again, calculate the minimum area subject to constrained volume. This time I'll show the calculation since the result is less obvious. I chose to instead minimize the ratio [math]R=[/math][math]A/V[/math] instead of [math]A[/math], since it simplifies the math, and is equivalent.[math]R=2(\frac{1}{h}+\frac{1}{r})[/math],Now do Lagrange multipliers:[math]L(r,h,\lambda)=R(r,h)+\lambda(\pi r^2 h)[/math].Taking the partials, one finds that the relationship between [math]h[/math] and [math]r[/math] is [math]h=2r[/math]. In this case you can check that the surface area of the "best case" cylinder is [math]3\sqrt[3]{2\pi}[/math].The sphere is the easiest case, since there's only one parameter, the radius, to vary.[math]V_{sphere}=\frac{4}{3}\pi r^3[/math], [math]A[/math][math]_{sphere}=4\pi r^2[/math].This means the surface area of a unit-volume sphere is [math]\sqrt[3]{36 \pi}[/math].So now we just have to compare the answers. Approximately, the answers are 6.0 for the cube, 5.5 for the cylinder, and 4.8 for the sphere.So the sphere clearly wins in terms of smallest surface area.However, there is also a well-established result that the sphere has the smallest surface area of any solid with fixed volume. So if you had known this, you could have answered this question without doing any of this calculation. This result explains why bubbles form spheres rather than cubes or cylinders, since the surface tension in the bubble's film tries to make the surface area as small as possible, while the air inside the bubble has a fixed volume.
What are the Genuine fresher job consultancies in Hyderabad?
If you are looking for some good and genuine job consultants in Hyderabad, then I can suggest one for you. Kinetic recruitment has a very good network with many reputed IT companies operating in Hyderabad. They have a good market reputation and offer job consultancy services especially for IT and Management jobs in Hyderabad.They have experienced and motivated HR team to take care of. So personally I would suggest Kinetic Recruitment Services if you are looking for domestic job consultancies in Hyderabad.Link:http://kineticrecruitment.co/con...Whatever placement agency you contact make sure to check the followingThe consultancy should have a physical office.A working websiteAsk for the list of companies they cater the servicesCheck for fees (Genuine ones do not charge from candidates)Check for any frauds on their name.Verify on internet about them thoroughly….One important note to mention is the proper resume before your job. Prepare a good resume or get it done with the consultant before applying for the jobAll the best!:)
What is a “valve overlap”?
Valve Overlap is the time during which both the inlet and exhaust valves remain open at the same time.Theoretically the inlet and exhaust valves, open and closes instantaneously at the dead centres. But what actually happens is that, these valves open/close, before and after the dead centres.The inlet valve opens before Top dead centre and closes after bottom dead centre. Tis is done so as to get maximum charge inside the cylinder. In order to get maximum inlet charge at the earliest moment of intake stroke, inlet valve is opened early. The kinetic energy of the moving charge at the end of the intake stroke is used to produce a ramming effect by closing the inlet valve after BDC. The ramming effect increases volumetric efficiency.The exhaust valve opens before BDC so as to exhaust the combustion product efficiently. By virtue of its excess pressure above atmosphere some exhaust gas leaves the cylinder. This allows the exhaust gas to flow freely from the cylinder by the time the piston commences the exhaust stroke. Again, by closing the exhaust valve after TDC, the kinetic energy of the exhaust gas can be utilised to assist in maximum exhausting of the gas. In the process inlet valve begins to open before the exhaust valve closes - and this is called VALVE OVERLAP.Thank you.Engine GeekThakur Prateek SinghImages: Google.Source: Automotive engines. Tata McGraw Hill
How can I delete my wireless router's history?
If you want to delete wireless router history then you need to access the router,Access The Router:-Find the default gateway/IP number/IP addressGo to command prompt, type "ipconfig"look at the default gateway.The IP number is listed by ipconfig under IP Address and Physical Address.For example 192.xxx.x.xDeleting History steps;-Open a web browser(Such as internet explorer/google chrome).Type the default gateway into a web browser.you should now be prompted for a user name and password.Enter your user name and password,and click your login button.Find Status Button or Advance button from navigation bar and click on it.Note:- This name(status or Advance) may be different for you because it depends on your router.6. click system log or administration Event log.7. click on the clear log button.This leads you clearing your router history.If you have more issues related to router then i suggest you to visit Router Archives | Fixingblog.comHave a nice day
Can I use my smart phone to operate my garage door opener?
Yes ofcourse! thanks to modern technologies and rapid advancements in mobile phone platforms. It sounds like something right out science-fiction but with the right phone and apps you can connect your phone to your garage door opener and get it opening and closing.The great thing about this method of controlling your garage door is that you don’t have to carry around another remote control that you are more likely to either lose or leave in your car overnight. We all have our Smartphones at arm’s length these days, and being able to carry out such control on your Android means less carriage and more efficiency.Learn more:Ben Garage Door Opener
Can valves control the flow rate in a piping system? How?
Question : Can valves control the flow rate in a piping system? How?Let us split this questionQuestion : Can valves control the flow rate in a piping system?Response : Yes. Globe valves are used to control the flow rate. Globe valves are like control valves, but require to be operated manually i.e. A globe valve with actuator becomes a Control Valve, though control valve has some additional parameters in designing it.How?All valves have a “gate”, which throttles the flow. In case of Globe valve it is smooth throttling ( the operating wheel can be adjusted to control the flow rate i.e. to increase & decrease the throttling) and very effective. Gate valves are generally used for STOP & START operations. Check valve to contain reverse flow of process liquid. Ball valves are quarter turn valves, used where firesafe design is required (quick opening & closing).Added in response to comment of Mr. Dennis Hoffmann on 24-Oct-2016It is a practice for process reasons to have more ball valves in pipingunless it is a utility services, in which gate valves are more used. If gate valves are used in process piping, may be as a replacement, then it is a dangerous trend for it would be difficult to close each valve & the time spent is too precious to be lost in case of incident / accident or fire. If gate valves are more in the piping system, then it requires a thorough relook at the design.Gate valves may find its numbers in petro-chemical plants & also in chemical plants.Christmass Tree valves are basically gate valve configuration, so does the well head valves, Blowout Preventer. This is done to ensure positive closureIn process unit operations, ball valves score & a must. Here if you find more gate valves, review the process design again & immediately !!! by a qualified & experienced Consulting Engineer with experience in design.
Why electric bulbs are not filled with air and which gas is present in them?
There is no vacuum in the electric bulb. On the contrary, argon gas or argon gas mixed with a little nitrogen is filled in the bulb under some pressure. Years ago there was a practice to leave vacuum inside the bulb so as to prevent the burning of tungsten filament in the temperature of 2000° Celsius inside the bulb. But at such a high temperature tungsten filament starts losing its atoms. Or, to be precise twisted strands of tungsten filament start ‘evaporating’ slowly. As the escaping particles of burnt tungsten settle on the transparent glass of the bulb, accumulating carbon becomes an obstruction to the light.Ultimately a situation comes about in which although the bulb is lit it does not throw much light in the room. Also, continuously ‘evaporating’ filament of tungsten may not last for a long time. A well-known American chemist named Erwin Lang-Moore invented two methods in 1913 to bring an end to both these problems: (1) He twisted the strands of tungsten filament weaving them into a plait which till now were in the form of spring like coils. Plaiting made the tungsten filament more durable. (2) He replaced the practice of leaving vacuum in the bulbs with that of filling them up with nitrogen or argon. Argon is an inert gas which does not give rise to any chemical reaction and so would not affect the working of tungsten filament. At the same time the pressure of Argon gas would almost prevent ‘evaporation’ of the filament.It is because of the above two inventions that a present day electric bulb has useful life of about 1,000 hours.I suggest you buy green energy lights (something like this Green Lux Energy LED A19 - 60- Watt Equivalent (10W)) It will save you money for bills, and its ecological