Плоштина и волумен на геометриски тела

Подготвителни задачи за тест II-ра година

1. Presmetaj ja plo{tinata na pravilna ~etiristrana potse~ena piramida so onovni rabovi 15 cm, 5cm i visina 12cm.                                                                                                    (15)

2. Plo{tinata na cilindar e 266p cm², a perimetarot na osnovata e 14p cm. Presmetaj go volumenot na cilindarot.                                                                                                           (12)

3. Ako rabot na kockata se zgolemi za 3cm, plo{tinata se zgolemuva za 198cm². Presmetaj ja plo{tinata na kockata.                                                                                                               (10)

4. Presmetaj ja plo{tinata i volumenot na kvadar, zadaden so osnovni rabovi a=4cm, b=3cm i dijagonala D=13cm.          

5. Presmetaj plo{tina i volumen na prava tristrana prizma ako site rabovi se so dol`ina 8 cm.                                                                                                                                                      (12)

6. Osnovniot rab na pravilna ~etiristrana piramida e 14 cm, visina 15 cm. Presmetaj ja plo{tinata na piramidata.                                                                                                         (15)

7. Presmetaj ja plo{tinata na cilindar so volumen 112p cm³ i visina 7 cm.                     (12)

8. Plo{tinata na pogolemata osnova na potse~en konus e 100p cm² , visinata e 48 cm, a odnosot na radiusite na pogolemata i pomalata osnova e 5:4. Presmetaj ja plo{tinata na potse~eniot konus.                                                                                                                         (15)

9. Presmetaj go volumenot na piramida so osnova kvadrat,  zadaden so visina H=7cm, a bo~niot rab e za 1cm pogolem od osnovniot rab.                                                                       (15)

10. Presmetaj go volumenot na cilindar so plo{tina 324p cm² i odnosot na visinata i radiusot e 7:2.  

11. Presmetaj go volumenot na konus ako bo~nata plo{tina mu e 240p cm² so visina 16 cm.

12. Presmetaj ja prostornata dijagonala na pravilna ~etiristrana potse~ena piramida so osnovni rabovi 7cm i 5cm i visina 3cm.                                                                                (15)
13. Kolku e rabot na kockata ako volumenot se zgolemi za 218 cm³ koga sekoj rab se zgolemuva za 2 cm.                                                                                                                          (12)

14. Presmetaj ja plo{tinata na kvadar so rabovi 14cm, 8cm i volumen 2912 cm³.                        (10)                                                                                               
15. Presmetaj ja plo{tinata na potse~en konus so bo~na plo{tina 85p cm², visina 4cm i generatrisa 5cm.                                                                                                                            (15)

16. Presmetaj ja plo{tinata i volumenot na kocka, so prostorna dijagonala 16cm.         (10)

17. Volumenot na kvadar e 120 cm³ i visina 5 cm, a osnovnite rabovi se odnesuvaat 3:2. Koloku e plo{tinata na kvadarot?                                                                                                 (12)

18. Presmetaj ja bo~nata plo{tina na cilindar ako negovata plo{tina e 84p cm², a visinata mu e pogolema 5 cm od dijametarot na osnovata.                                                             (12)

19. Presmetaj go volumenot na konus ako negovata plo{tina e 560p cm² i generatrisa 26 cm.
20. Volumenot  na kocka e 64 cm³.Kolku e prostornata dijagonala?                                       (10)