{"paper":{"id":"site-2666","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":11,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2666/zad/3161","paper_id":"site-2666","number":"3161","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Przekątna prostopadłościanu o wymiarach 3 x 4 x 5 ma długość A. 2 pierwiastki z 5, B. 2 pierwiastki z 3, C. 5 pierwiastków z 2, D. 2 pierwiastki z 15","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-3161.svg","solution_image":"img/site/2666/rozw-3161.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/3162","paper_id":"site-2666","number":"3162","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Suma długości wszystkich krawędzi sześcianu jest równa 24. Objętość tego sześcianu jest równa A. 64, B. 27, C. 24, D. 8","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-3162.svg","solution_image":"img/site/2666/rozw-3162.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/3163","paper_id":"site-2666","number":"3163","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Przekątna sześcianu ma długość 3. Pole powierzchni całkowitej tego sześcianu jest równe A. 54, B. 36, C. 18, D. 12","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-3163.svg","solution_image":"img/site/2666/rozw-3163.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/3164","paper_id":"site-2666","number":"3164","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Pole powierzchni całkowitej sześcianu jest równe 24 cm^2. Objętość tego sześcianu jest równa A. 8 cm^3, B. 16 cm^3, C. 27 cm^3, D. 64 cm^3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-3164.svg","solution_image":"img/site/2666/rozw-3164.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/3165","paper_id":"site-2666","number":"3165","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Przekątna prostopadłościanu o wymiarach 2x3x5 ma długość A. pierwiastek z 13, B. pierwiastek z 29, C. pierwiastek z 34, D. pierwiastek z 38","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-3165.svg","solution_image":"img/site/2666/rozw-3165.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/3300","paper_id":"site-2666","number":"3300","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dany jest sześcian ABCDEFGH. Siatką ostrosłupa czworokątnego ABCDE jest A., B., C., D.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-3300.svg","solution_image":"img/site/2666/rozw-3300.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/5324","paper_id":"site-2666","number":"5324","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Przekątna sześcianu ma długość 4√3. Pole powierzchni tego sześcianu jest równe A. 96; B. 24√3; C. 192; D. 16√3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-5324.svg","solution_image":"img/site/2666/rozw-5324.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/5487","paper_id":"site-2666","number":"5487","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Przekątna sześcianu ma długość 5√3. Wtedy objętość tego sześcianu jest równa A. 125 B. 75 C. 375 D. 125","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-5487.svg","solution_image":"img/site/2666/rozw-5487.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/5785","paper_id":"site-2666","number":"5785","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Pole powierzchni całkowitej sześcianu jest równe 12. Suma długości wszystkich krawędzi tego sześcianu jest równa A. 6√2 B. 3√2 C. 12√2 D. 8√2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-5785.svg","solution_image":"img/site/2666/rozw-5785.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/6746","paper_id":"site-2666","number":"6746","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dany jest prostopadłościan ABCDEFGH, w którym prostokąty ABCD i EFGH są jego postawami. Odcinek BH jest przekątną tego prostopadłościanu. [rysunek] Na którym rysunku prawidłowo narysowano, oznaczono i podpisano kąt α pomiędzy przekątną BH prostopadłościanu a jego ścianą boczną ADHE? Zaznacz właściwą odpowiedź spośród podanych. A. α=∠BHD [rysunek] B. α=∠BHE [rysunek] C. α=∠BHA [rysunek] D. α=∠ BHK [rysunek].","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-6746.svg","solution_image":"img/site/2666/rozw-6746.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2666/zad/6748","paper_id":"site-2666","number":"6748","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dane są dwa prostopadłościany podobne: B_1 oraz B_2. Objętość prostopadłościanu B_1 jest równa V, a objętość prostopadłościanu B_2 jest równa 27V. Pole powierzchni całkowitej prostopadłościanu B_1 jest równe P. Dokończ zdanie. Wybierz odpowiedź A, B albo C oraz jej uzasadnienie A. 27P B. 9P C. 3√3 ponieważ stosunek pól powierzchni całkowitych prostopadłościanów podobnych jest równy 1. stosunkowi objętości tych prostopadłościanów. 2. pierwiastkowi kwadratowemu ze stosunku objętości tych prostopadłościanów. 3. kwadratowi stosunku długości odcinków\\v1exodpowiadających w obu prostopadłościanach.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2666/zad-6748.svg","solution_image":"img/site/2666/rozw-6748.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}