Question

Aflati aria totala a unui cub cu diagonala mai lunga cu 1 cm decit muchia lui .

Answer 1

notam muchia cu a
diagonala=a√3
a√3-a=1
a(√3-1)=1
a=1/(√3-1)=(√3+1)/(√3-1)(√3+1)=(√3+1)/(3-1)=(√3+1)/2
Acub=6 × a²= 6×[(√3+1)/2]²= 6×(√3+1)²/4=3×(3+1+2√3)/2=3×(4+2√3)/2=
=3×(2+√3)=6+3√3 cm²