Objem ti hovorí, koľko miesta nejaká vec zaberá alebo koľko... Show more
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Updated Mar 27, 2026
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Ako vypočítať objem kocky a kvádra
1 / 7
Čo sú kocka a kváder
Predstav si hraciu kocku - má všetky steny rovnaké a všetky hrany sú rovnako dlhé. To je kocka. Všetky jej steny sú štvorce a je úplne pravidelná.
Kváder je ako krabica od topánok alebo tehla. Má steny tvaru obdĺžnika a tri rôzne dĺžky hrán - dĺžku, šírku a výšku. Niekedy môžu byť niektoré strany rovnaké, ale nie všetky.
Oba tieto tvary majú 6 stien a používajú sa všade okolo nás. Od škatúľ na hračky až po budovy!
💡 Tip: Pozri sa okolo seba - väčšina vecí má tvar kocky alebo kvádra!
Jednotky objemu a základné pojmy
Objem meriame v špeciálnych jednotkách s malou trojkou hore. Najčastejšie používame kubické centimetre (cm³), kubické decimetre (dm³) a kubické metre (m³).
Dôležité je zapamätať si, že 1 dm³ = 1 liter. Takže keď počítaš, koľko vody sa zmestí do nádoby, stačí vypočítať objem v dm³ a máš to rovno v litroch!
Hrana je čiara, kde sa stretávajú dve steny. Kocka má všetky hrany rovnaké, kváder má tri rôzne dĺžky hrán.
💡 Zapamätaj si: Vždy musíš mať všetky rozmery v rovnakých jednotkách pred výpočtom!
Objem kocky - vzorec a výpočet
Objem kocky je super jednoduchý! Stačí vynásobiť dĺžku hrany trikrát samu so sebou: V = a × a × a alebo kratšie V = a³.
Skúsme si to na príklade: Máš kocku s hranou 3 cm. Jej objem je 3 × 3 × 3 = 27 cm³.
Prečo násobíme trikrát? Lebo potrebujeme zistiť priestor vo všetkých troch smeroch - dĺžka, šírka aj výška. U kocky sú všetky rovnaké, preto násobíme tú istú hodnotu trikrát.
💡 Nezabudni: Výsledok má vždy jednotky s trojkou hore (cm³, dm³, m³)!
Objem kvádra - vzorec a výpočet
Pri kvádri násobíme všetky tri rôzne rozmery: V = a × b × c, kde a je dĺžka, b je šírka a c je výška.
Napríklad: Kváder má dĺžku 5 cm, šírku 2 cm a výšku 4 cm. Jeho objem je 5 × 2 × 4 = 40 cm³.
Ak riešiš úlohu s akváriom, pamätaj si, že výsledok v dm³ môžeš rovno prepísať na litre. Akvárium s rozmermi 8×3×5 dm má objem 120 dm³, čiže sa do neho zmestí 120 litrov vody.
💡 Praktický tip: Pri prevode jednotiek si najprv všetko prepočítaj do tej istej jednotky - buď všetko na cm, alebo všetko na dm!
Riešené príklady krok za krokom
Pozrime si pár praktických úloh. Pri každej si najprv zapíš, čo vieš, potom vzorec a nakonec vypočítaj.
Príklad 1: Kocka s hranou 7 cm má objem 7³ = 343 cm³.
Príklad 2: Akvárium 8×3×5 dm má objem 8×3×5 = 120 dm³ = 120 litrov.
Príklad 3: Pozor na prevod jednotiek! Krabica 2 dm × 10 cm × 1 dm. Najprv prevedi: 20 cm × 10 cm × 10 cm = 2000 cm³.
💡 Dôležité: Vždy kontroluj, či máš všetky rozmery v rovnakých jednotkách!
Tipy na skúšku a zhrnutie
Zapamätaj si tieto základne vzorce: objem kocky je V = a³ a objem kvádra je V = a × b × c.
Najčastejšie chyby: zabudnuté jednotky s trojkou, miešanie jednotiek (cm s dm) a chyby pri násobení. Vždy si najprv zapíš vzorec a potom dosadzuj čísla.
Užitočné prevody: 1 m³ = 1000 dm³, 1 dm³ = 1000 cm³, a hlavne 1 dm³ = 1 liter. Toto sa ti bude hodiť pri úlohách s vodou.
💡 Pred testom: Precvič si pár príkladov s prevodom jednotiek - to je najčastejší problém!
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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
Ako vypočítať objem kocky a kvádra
Objem ti hovorí, koľko miesta nejaká vec zaberá alebo koľko sa do nej zmestí - napríklad koľko vody sa zmestí do akvária. Dnes si ukážeme, ako jednoducho vypočítať objem kocky a kvádra pomocou základných vzorcov.
Čo sú kocka a kváder
Predstav si hraciu kocku - má všetky steny rovnaké a všetky hrany sú rovnako dlhé. To je kocka. Všetky jej steny sú štvorce a je úplne pravidelná.
Kváder je ako krabica od topánok alebo tehla. Má steny tvaru obdĺžnika a tri rôzne dĺžky hrán - dĺžku, šírku a výšku. Niekedy môžu byť niektoré strany rovnaké, ale nie všetky.
Oba tieto tvary majú 6 stien a používajú sa všade okolo nás. Od škatúľ na hračky až po budovy!
💡 Tip: Pozri sa okolo seba - väčšina vecí má tvar kocky alebo kvádra!
Sign up to see the contentIt's free!
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Improve your grades
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Jednotky objemu a základné pojmy
Objem meriame v špeciálnych jednotkách s malou trojkou hore. Najčastejšie používame kubické centimetre (cm³), kubické decimetre (dm³) a kubické metre (m³).
Dôležité je zapamätať si, že 1 dm³ = 1 liter. Takže keď počítaš, koľko vody sa zmestí do nádoby, stačí vypočítať objem v dm³ a máš to rovno v litroch!
Hrana je čiara, kde sa stretávajú dve steny. Kocka má všetky hrany rovnaké, kváder má tri rôzne dĺžky hrán.
💡 Zapamätaj si: Vždy musíš mať všetky rozmery v rovnakých jednotkách pred výpočtom!
Sign up to see the contentIt's free!
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Improve your grades
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Objem kocky - vzorec a výpočet
Objem kocky je super jednoduchý! Stačí vynásobiť dĺžku hrany trikrát samu so sebou: V = a × a × a alebo kratšie V = a³.
Skúsme si to na príklade: Máš kocku s hranou 3 cm. Jej objem je 3 × 3 × 3 = 27 cm³.
Prečo násobíme trikrát? Lebo potrebujeme zistiť priestor vo všetkých troch smeroch - dĺžka, šírka aj výška. U kocky sú všetky rovnaké, preto násobíme tú istú hodnotu trikrát.
💡 Nezabudni: Výsledok má vždy jednotky s trojkou hore (cm³, dm³, m³)!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Objem kvádra - vzorec a výpočet
Pri kvádri násobíme všetky tri rôzne rozmery: V = a × b × c, kde a je dĺžka, b je šírka a c je výška.
Napríklad: Kváder má dĺžku 5 cm, šírku 2 cm a výšku 4 cm. Jeho objem je 5 × 2 × 4 = 40 cm³.
Ak riešiš úlohu s akváriom, pamätaj si, že výsledok v dm³ môžeš rovno prepísať na litre. Akvárium s rozmermi 8×3×5 dm má objem 120 dm³, čiže sa do neho zmestí 120 litrov vody.
💡 Praktický tip: Pri prevode jednotiek si najprv všetko prepočítaj do tej istej jednotky - buď všetko na cm, alebo všetko na dm!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Riešené príklady krok za krokom
Pozrime si pár praktických úloh. Pri každej si najprv zapíš, čo vieš, potom vzorec a nakonec vypočítaj.
Príklad 1: Kocka s hranou 7 cm má objem 7³ = 343 cm³.
Príklad 2: Akvárium 8×3×5 dm má objem 8×3×5 = 120 dm³ = 120 litrov.
Príklad 3: Pozor na prevod jednotiek! Krabica 2 dm × 10 cm × 1 dm. Najprv prevedi: 20 cm × 10 cm × 10 cm = 2000 cm³.
💡 Dôležité: Vždy kontroluj, či máš všetky rozmery v rovnakých jednotkách!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Tipy na skúšku a zhrnutie
Zapamätaj si tieto základne vzorce: objem kocky je V = a³ a objem kvádra je V = a × b × c.
Najčastejšie chyby: zabudnuté jednotky s trojkou, miešanie jednotiek (cm s dm) a chyby pri násobení. Vždy si najprv zapíš vzorec a potom dosadzuj čísla.
Užitočné prevody: 1 m³ = 1000 dm³, 1 dm³ = 1000 cm³, a hlavne 1 dm³ = 1 liter. Toto sa ti bude hodiť pri úlohách s vodou.
💡 Pred testom: Precvič si pár príkladov s prevodom jednotiek - to je najčastejší problém!
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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Students love us — and so will you.
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