Question

Daca dimendiunile unui paralelipiped dreptunghic sunt direct proportionale cu nr 3, 4, si 6 iar suma lor este 26 cm atunci Volumul este?

Answer 1

Fie a, b, c dimensiunile paralelipipedului.

$\it \{a,\ b,\ c\}\sim \{3,\ 4,\ 6\} \Rightarrow \dfrac{a}{3}=\dfrac{b}{4}=\dfrac{c}{6} =\dfrac{a+b+c}{3+4+6}=\dfrac{26}{13}=2 \Longrightarrow \\ \\ \\ \Longrightarrow \begin{cases}\it \dfrac{a}{3}=2 \Rightarrow a=3\cdot2=6cm\\ \\ \it \dfrac{b}{4}=2 \Rightarrow b=4\cdot2=8cm\\ \\ \it \dfrac{c}{6}=2 \Rightarrow c=6\cdot2=12cm\end{cases}\\ \\ \\ \mathcal{V}=a\cdot b\cdot c= 6\cdot8\cdot12=6\cdot96=576cm^3$