Question

Raportul ariilor a 2 tetraede regulate este 4 pe 9 afla raportul volumelor tetraedelor

Answer 1

       
$\text{Consideram doua figuri geometrice in spatiu, care sunt} \; \bold{asemenea}, \\ \text{nu neaparat} \; \bold{tetraedre \; regulate}. \\ \text{In acest caz, raportul ariilor celor doua figuri = raportul patratelor} \\ \text{a doua laturi corespondente} \\ \text{Raportul Volumelor celor doua figuri = raportul cuburilor} \\ \text{a doua laturi corespondente} \\ Formulele \;sunt: \\ \\ \frac{A_1}{A_2}= (\frac{l_1}{l_2} )^{2} \\ \\ \frac{V_1}{V_2}= (\frac{l_1}{l_2} )^{3}$

$Rezolvare: \\ \\ \frac{A_1}{A_2}= (\frac{l_1}{l_2} )^{2} = \frac{4}{9} \\ \\ =>\frac{l_1}{l_2}= \sqrt{\frac{4}{9} } =\frac{2}{3} \\ \\ \frac{V_1}{V_2}= (\frac{l_1}{l_2} )^{3}= (\frac{2}{3})^{3} =\boxed{\frac{8}{27}}$