Question

Calcule o volume de um paralelepipedo retangulo que suas dimensões sao proporcionais a 9,12,20, e sua diagonal mede 100m

Answer 1

V = a . b . c
V= 9.12.20= 2.160 m³

Answer 2

Sejam a, b e c suas dimensões.

$\frac{a}{9}= \frac{b}{12}= \frac{c}{20} \\ \\ \frac{a^2}{81}= \frac{b^2}{144}= \frac{c^2}{400} \\ \\ \frac{a^2+b^2+c^2}{181+144+400}= \frac{a^2}{81}= \frac{b^2}{144}= \frac{c^2}{400} \\ \\ d= \sqrt{a^2+b^2+c^2} \\ \\ 100= \sqrt{a^2+b^2+c^2} \\ \\ a^2+b^2+c^2=100^2=10000 \\ \\ \frac{1000}{625}= \frac{a^2}{81} \\ \\ \frac{a^2}{81} =16 \\ \\ a^2=81.16 \\ \\ a=4.9 \\ \\ a=36m \\ \\ \frac{b^2}{144}=16 \\ \\ b^2=16.144 \\ \\ b=4.12 \\ \\ b=48m \\ \\ \frac{c^2}{400}=16$

$\frac{c^2}{400}=16 \\ \\ c^2=16.400 \\ \\ c=4.20 \\ \\ c=80m \\ \\ V=abc \\ \\ V= 36.48.80 \\ \\ V=138.240m^3$