Răspuns :
[tex]\text{Voi nota prisma cu ABCDA'B'C'D'.Prin urmare vom avea AA'=40}\\
\text{cm si AB=10 cm.}\\
a)A_l=4\cdot L\cdot h\\
A_l=4\cdot 40\cdot 10=1600\ cm^2\\
b)\text{Aflam volumul vazei:}\\
V=A_b\cdot h\\
V=L^2 \cdot h\\
V=100\cdot 40=4000\ cm^3=4\ litri\\
\text{Aflam\ inaltime\ initiala\ la\ care\ se\ ridica\ apa\ in\ vaza:}\\
V_{ap\breve{a}}=A_b\cdot h_{ap\breve{a}}\\
3000=L^2\cdot h_{ap\breve{a}}\\
3000=100\cdot h_{ap\breve{a}}\Rightarrow h_{ap\breve{a}}=30\ cm\\
\text{Calculam volumul cuburilor:}\\
[/tex]
[tex]V_{cuburi}=4\cdot l^3(\text{unde l este latura cubului})\\ V_{cuburi}=256\ cm^3\\ \text{Aflam volumul total}\\ V_{total}=V_{cuburi}+V_{ap\breve{a}}\\ V_{total}=256+3000=3256\ cm^3\\ \text{Aflam inaltimea la care se ridica apa.Voi nota cu h' aceasta inaltime.}\\ V_{total}=A_b\cdot h'\\ 3256=100\cdot h'\Rightarrow \boxed{h'=32,56\ cm}\\ [/tex]
[tex]V_{cuburi}=4\cdot l^3(\text{unde l este latura cubului})\\ V_{cuburi}=256\ cm^3\\ \text{Aflam volumul total}\\ V_{total}=V_{cuburi}+V_{ap\breve{a}}\\ V_{total}=256+3000=3256\ cm^3\\ \text{Aflam inaltimea la care se ridica apa.Voi nota cu h' aceasta inaltime.}\\ V_{total}=A_b\cdot h'\\ 3256=100\cdot h'\Rightarrow \boxed{h'=32,56\ cm}\\ [/tex]
