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
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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!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the 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.
Most popular content in Matematika
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Can't find what you're looking for? Explore other subjects.
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
Join milions of students
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 specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the 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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user