Geometrijska telesa so vse okrog nas – od škatle za... Show more
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Updated Apr 10, 2026
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Razumevanje Geometrijskih Teles
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Uvod v geometrijska telesa
Predstavljaj si razliko med risbo kvadrata na papir in pravo kocko v rokah. Geometrijska telesa so tridimenzionalne oblike, ki jih lahko prijameš in držiš, ker imajo dolžino, širino IN višino.
Vsako geometrijsko telo sestavlja več mejnih ploskev (ravnih površin), ki se stikajo v robovih (črtah). Tam, kjer se srečajo trije ali več robov, nastane oglišče – to je "vogal" telesa.
Če geometrijsko telo "razgrnemo" kot darilo, dobimo mrežo telesa. To je kot da bi razrezali škatlo in jo razporedili po mizi. Površina nam pove, koliko papirja potrebujemo za ovijanje celega telesa, prostornina pa, koliko vode lahko vlijemo vanj.
💡 Pomni: Površina je "obleka" telesa (enota: cm²), prostornina pa "vsebina" telesa (enota: cm³)!
Kocka – popolno geometrijsko telo
Kocka je najlažje geometrijsko telo za razumevanje, ker je popolnoma simetrična. Sestavlja jo šest popolnoma enakih kvadratov, ima 12 enako dolgih robov (dolžina a) in 8 oglišč.
Obstaja kar 11 različnih mrež kocke, vendar vse vsebujejo 6 enakih kvadratov, ki se lahko pravilno zložijo v kocko. To je super za preverjanje na testih!
Površina kocke je preprosta: ker ima 6 enakih kvadratnih ploskev, samo pomnožimo ploščino enega kvadrata s 6. Formula je P = 6 × a².
Prostornina kocke je še lažja: pomnožimo rob sam s sabo trikrat. Formula je V = a³ (beremo "a na kub").
💡 Praktičen nasvet: Če imaš kocko z robom 2 cm, je njena površina 6 × 4 = 24 cm², prostornina pa 8 cm³!
Kvader – podolgovata kocka
Kvader je kot podolgovata škatla – ima še vedno 6 mejnih ploskev (pravokotnikov), 12 robov in 8 oglišč, vendar robovi niso vsi enako dolgi.
Označimo tri različne dolžine robov z a (dolžina), b (širina) in c (višina). Nasproti ležeče ploskve so vedno enake – to pomeni, da imamo 3 pare enakih pravokotnikov.
Površina kvadra je malo bolj zapletena, ker moramo sešteti ploščine vseh šestih ploskev: P = 2. Dvojka je tu zato, ker imamo od vsakega pravokotnika po dva.
Prostornina kvadra pa je preprosta: pomnožimo vse tri dimenzije skupaj. Formula je V = a × b × c.
💡 Pomni: Kvader je kot tri različne dimenzije, ki se množijo med sseboj za prostornino!
Praktični primeri z izračuni
Poglejmo si konkretna primera, ki jih boš srečal na testih!
Primer s kocko: Igralna kocka z robom 2 cm ima površino P = 6 × (2)² = 6 × 4 = 24 cm² in prostornino V = 2³ = 8 cm³.
Primer s kvadrom: Škatla za čevlje (30 cm × 20 cm × 10 cm) potrebuje P = 2(30×20 + 30×10 + 20×10) = 2(600 + 300 + 200) = 2200 cm² kartona. Njena prostornina je V = 30 × 20 × 10 = 6000 cm³.
Vedno najprej izpiši podatke, preveri enote in uporabi pravilno formulo. Pri površini dobiš kvadratne enote (cm²), pri prostornini pa kubične (cm³).
💡 Koristno za življenje: 1 liter = 1 dm³, torej kocka z robom 10 cm sprejme natanko 1 liter vode!
Hiter povzetek za uspeh na testu
Kocka: 6 enakih kvadratov, vsi robovi enaki (a)
- Površina: P = 6 × a²
- Prostornina: V = a³
Kvader: 6 pravokotnikov, 3 različne dimenzije (a, b, c)
- Površina: P = 2
- Prostornina: V = a × b × c
Ključne razlike: Površina je "obleka" (cm²), prostornina "vsebina" (cm³). Mreža je razgrnjeno telo – pri kocki 6 enakih kvadratov, pri kvadru 6 pravokotnikov v 3 parih.
Na testih pazi na enote in vedno preveri, ali imaš smiselne rezultate!
💡 Za odličen uspeh: Naredi si tabelo s formulami in jo uporabljaj, dokler se jih ne naučiš na pamet!
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Stefan S
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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
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Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Razumevanje Geometrijskih Teles
Geometrijska telesa so vse okrog nas – od škatle za čevlje do igralne kocke! To so 3D oblike, ki imajo dolžino, širino in višino ter zavzamejo pravi prostor. Naučili se boste izračunavati njihovo površino in prostornino.
Uvod v geometrijska telesa
Predstavljaj si razliko med risbo kvadrata na papir in pravo kocko v rokah. Geometrijska telesa so tridimenzionalne oblike, ki jih lahko prijameš in držiš, ker imajo dolžino, širino IN višino.
Vsako geometrijsko telo sestavlja več mejnih ploskev (ravnih površin), ki se stikajo v robovih (črtah). Tam, kjer se srečajo trije ali več robov, nastane oglišče – to je "vogal" telesa.
Če geometrijsko telo "razgrnemo" kot darilo, dobimo mrežo telesa. To je kot da bi razrezali škatlo in jo razporedili po mizi. Površina nam pove, koliko papirja potrebujemo za ovijanje celega telesa, prostornina pa, koliko vode lahko vlijemo vanj.
💡 Pomni: Površina je "obleka" telesa (enota: cm²), prostornina pa "vsebina" telesa (enota: cm³)!
Sign up to see the contentIt's free!
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Kocka – popolno geometrijsko telo
Kocka je najlažje geometrijsko telo za razumevanje, ker je popolnoma simetrična. Sestavlja jo šest popolnoma enakih kvadratov, ima 12 enako dolgih robov (dolžina a) in 8 oglišč.
Obstaja kar 11 različnih mrež kocke, vendar vse vsebujejo 6 enakih kvadratov, ki se lahko pravilno zložijo v kocko. To je super za preverjanje na testih!
Površina kocke je preprosta: ker ima 6 enakih kvadratnih ploskev, samo pomnožimo ploščino enega kvadrata s 6. Formula je P = 6 × a².
Prostornina kocke je še lažja: pomnožimo rob sam s sabo trikrat. Formula je V = a³ (beremo "a na kub").
💡 Praktičen nasvet: Če imaš kocko z robom 2 cm, je njena površina 6 × 4 = 24 cm², prostornina pa 8 cm³!
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Kvader – podolgovata kocka
Kvader je kot podolgovata škatla – ima še vedno 6 mejnih ploskev (pravokotnikov), 12 robov in 8 oglišč, vendar robovi niso vsi enako dolgi.
Označimo tri različne dolžine robov z a (dolžina), b (širina) in c (višina). Nasproti ležeče ploskve so vedno enake – to pomeni, da imamo 3 pare enakih pravokotnikov.
Površina kvadra je malo bolj zapletena, ker moramo sešteti ploščine vseh šestih ploskev: P = 2. Dvojka je tu zato, ker imamo od vsakega pravokotnika po dva.
Prostornina kvadra pa je preprosta: pomnožimo vse tri dimenzije skupaj. Formula je V = a × b × c.
💡 Pomni: Kvader je kot tri različne dimenzije, ki se množijo med sseboj za prostornino!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Praktični primeri z izračuni
Poglejmo si konkretna primera, ki jih boš srečal na testih!
Primer s kocko: Igralna kocka z robom 2 cm ima površino P = 6 × (2)² = 6 × 4 = 24 cm² in prostornino V = 2³ = 8 cm³.
Primer s kvadrom: Škatla za čevlje (30 cm × 20 cm × 10 cm) potrebuje P = 2(30×20 + 30×10 + 20×10) = 2(600 + 300 + 200) = 2200 cm² kartona. Njena prostornina je V = 30 × 20 × 10 = 6000 cm³.
Vedno najprej izpiši podatke, preveri enote in uporabi pravilno formulo. Pri površini dobiš kvadratne enote (cm²), pri prostornini pa kubične (cm³).
💡 Koristno za življenje: 1 liter = 1 dm³, torej kocka z robom 10 cm sprejme natanko 1 liter vode!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Hiter povzetek za uspeh na testu
Kocka: 6 enakih kvadratov, vsi robovi enaki (a)
- Površina: P = 6 × a²
- Prostornina: V = a³
Kvader: 6 pravokotnikov, 3 različne dimenzije (a, b, c)
- Površina: P = 2
- Prostornina: V = a × b × c
Ključne razlike: Površina je "obleka" (cm²), prostornina "vsebina" (cm³). Mreža je razgrnjeno telo – pri kocki 6 enakih kvadratov, pri kvadru 6 pravokotnikov v 3 parih.
Na testih pazi na enote in vedno preveri, ali imaš smiselne rezultate!
💡 Za odličen uspeh: Naredi si tabelo s formulami in jo uporabljaj, dokler se jih ne naučiš na pamet!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user