Surface area of a box using nets Khan Academy English Serbian

Surface area of a box using netsYouTube↗ IA↗(long shot)
Education 177.7K views 62 likes 15 dislikes 04 Sep 2015

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- [Voiceover] In a previous video, we figured out how

У претходном снимку смо одредили како

to find the surface area of this cereal box

одредити површину ове кутије за житарице

by figuring out the areas of each of the six surfaces

одређивањем површине сваке од шест страна

of the box, and then adding them all up.

кутије, а затим их сабирајући.

I'm going to do that again in this video,

Урадићу то поново у овом снимку,

but I'm going to do it by visualizing a net for the box.

али урадићу то сликовитим приказом мрежу кутије.

The way I think about a net of a box

Начин на који размишљам о мрежи кутије

like this, is what would happen if you were

попут ове је, шта ће се десити ако бисте

to cut the cardboard and then flatten it all out?

исекли картон а затим га полегли?

So what am I talking about?

Онда, о чему ја говорим?

Well, what we have here, we could imagine

Па, оно шта имамо овде, можемо замислити

making a cut in the box, and the cut could be,

сечење кутије, а рез може бити

let's see, I could make a cut back here,

да видимо, могу направити рез овде назад,

So I could make a cut right over there,

Дакле, могу начинити рез тачно тамо,

I could cut it...

могу је исећи...

I could cut it right like this, I could cut it like that.

Могу је исећи тачно овако, могу је исећи тако.

So if I just did that, this top flap would

Па, ако урадим тако, овај горњи део би

flap open so that would be able to come out

се отворио тако да би то могло изаћи напоље

like that, and then I could also

тако, а онда могу такође

make a cut for this side.

начинити рез за ову страну.

So I could make a cut back there,

Дакле, могу начинити рез тамо назад,

and I could make a cut right over here,

и могу начинити рез тачно овде,

and now this side could flap forward,

а сада ова страна може пасти између,

and I could do the same thing on

и могу урадити исто

this other side right over here.

са овом страном тачно овде.

Then that could flap forward,

Затим та може пасти између,

and then, the back side, I could draw it.

а онда, задња страна, могу је нацртати.

So I would also have a cut.

Дакле, такође бих имао рез.

I'll draw it as a dotted line because

Нацртаћу ту линију испрекидано јер

you're not supposed to be able to see this cut.

није предвиђено да будете у стању да видите овај рез.

But the corresponding cut to this one

Али одговарајући рез ове

on the side that we can't see,

стране коју не можемо видети,

we can draw it a little bit neater than that.

можемо нацртати то малчице лепше од тога.

The corresponding cut would be right back here.

Одговарајући рез би био тачно овде назад.

Right back there, and then a cut right over here.

Тачно тамо назад, а онда рез тачно овде.

And so what would happen

И онда, шта би се десило

if we were to flatten all of this out?

ако бисмо полегли све ово?

Well we would have,

Па, имали бисмо,

we would have the front of the box.

имали бисмо фронт кутије.

I'll try to draw this as neatly as I can.

Покушаћу да нацртам ово што леше могу.

So the front of the box looks like this.

Дакле, фронт кутије изгледа овако.

We would have this top flap, which looks like this

Имали бисмо овај горњи поклопац, који изгледа овако,

If we were to flatten it all out.

Ако бисмо требали да расклопимо све.

We have these two side flaps.

Имамо ове две стране расклопљене.

So that's a side flap.

Дакле, то је расклопљена страна.

That's a slide flap.

То је расклопљена страна.

And this is another, this side flap right over here.

А ово је друга, ова страна је расклопљена овде.

That's a side flap.

То је расклопљена страна.

Then we would have the bottom of the box.

Затим бисмо имали дно кутије.

So the bottom of the box is going to look like this.

Дакле, дно кутије ће изгледати овако.

The bottom of the box.

Дно кутије.

And then we have the back of the box.

А затим имамо позадину кутије,

That the bottom is going to be connected to.

са којом ће дно бити повезано.

We didn't cut that.

Нисмо исекли то.

So we have the back of the box.

Дакле, имамо позадину китије.

The back of the box looks like this.

Позадина кутије изгледа овако.

And there we have it.

И ту имамо то.

We've made the net.

Начинили смо мрежу.

This is what would happen if you

Ово је шта ће се десити ако

made the cuts that I talked about

начините резове о којима сам говорио

and then flatten the box out, it would look like this.

и онда расклопимо кутију, изгледаће овако.

Now how can we use this net to find the surface area?

Сада, како можемо употребити ову мрежу да одредимо површину?

Well we just need to figure out

Па, само треба да одредимо

the surface area of this shape now.

површину овог облика сада.

So how do we do that?

Онда, како ћемо урадити то?

Well we know a lot about the dimensions.

Па, знамо доста о димензијама.

We know that this width right over here,

Знамо да је ова ширина овде,

that this is ten centimeters.

да је она десет центиметара.

Ten centimeters from there to there.

Десет центиметара одавде до тамо.

We know the height, actually,

Знамо да висина, заправо,

going all the way from here all the way up.

иде целим путем одавде и све до горе.

Because the height of the box is 20 centimeters,

Пошто је висина кутије 20 центиметара,

so this is going to be 20 centimeters right over here.

тако да ће ово управо овде бити 20 центиметара.

And you have another 20 centimeters,

И имате још 20 центиметара,

you have another 20 centimeters right over here.

имате још 20 центиметара тачно овде.

And right over here if you like.

И тачно овде, ако желите.

And then you have, see the depth of the box

А затим имате, видите ширине кутије

is three centimeters, so this is three centimeters.

је три центиметара, дакле, ово је три центиметара.

Three centimeters, and then this is three centimeters.

Три центиметара, а затим је ово три центиметара.

And so what is the area,

И онда, колика је површина,

actually just let me do one region first.

заправо само ми дозволите да прво решим једну област.

What is the area of this entire region

Колика је површина ове целе области

that I am shading in with this blue color?

коју сенчим у овој плавој боји?

Well it's ten centimeters, that is,

Па, то је десет центиметара, то је,

I'll do a color that you can see a bit more easily.

узећу боју коју могу видети малчице лакше.

It is ten centimeters wide, ten centimeters.

То је десет центиметара дугачко, десет центиметара.

Times, what's the height?

Пута, колика је висина?

20, plus three, plus 20, plus three.

20, плус три, плус 20, плус три.

So that's going to be 40 plus six, so times 46 centimeters.

Дакле, то ће бити 40 плус шест, дакле, пута 46 центиметара.

That's this blue area.

То је плава област.

So that's going to be 460, 460 square centimeters.

Значи, то ће бити 460, 460 квадратних центиметара.

460 square centimeters, and now we just

460 квадратних центиметара, и сада само

have to figure out the area of the two flaps.

треба да одредимо површину два дела.

So this flap right over here

Значи, овај део овде

is 20 centimeters by three centimeters.

је 20 центиметара са три центиметра.

So that's 60 centimeters squared.

Значи, то је 60 квадратних центиметара.

So 60 centimeters squared,

Дакле, 60 центиметара квадратних

or 60 square centimeters I should say.

или 60 квадратних центиметара, да тако кажем.

And then this flap is going to have the exact same area.

А затим, овај део ће имати потпуно исту површину.

Another 60 square centimeters.

Још 60 квадратних центиметара.

60 square centimeters, and you add everything together.

60 квадратних центиметара и саберете све то.

We deserve a little bit of a drumroll.

Заслужујемо мало аплауза.

We get, well this is going to add up to

Добили смо, па, ово даје

580 square centimeters.

580 квадратних центиметара.

Which is the exact thing we got in the other video

Што је тачно оно што смо добили у другом снимку

where we didn't use a net, and you should just,

где нисмо користили мрежу, и требало би да будете,

it's nice to be able to do it either way.

добро је да будете у стању да решите на оба начина.

To be able to visualize the net

Да будете у стању да скицирате мрежу,

or to be able to look at this and think about

или да будете у стању да погледате ово и размислите о

the different sides, even the sides that

различитим странама, чак и странама које

you might not necessarily see.

можда не морате нужно да видите.

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