Question

Dado um poliedro retângulo de dimensões 4m, 3m, 10m, Calcule
A)a diagonal
B) area total
C)volume

Answer 1

A) Diagonal:

$d^2 = a^2 + b^2 + c^2 \\ \\ d^2 = 4^2 + 3^2 + 10^2 \\ \\ d^2 = 16 + 9 + 100 \\ \\ d^2 = 125 \\ \\ d = \sqrt{125} \\ \\ d = 5 \sqrt{5} ~ m$

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B) Área total:

$At = 2 . (ab + ac + bc) \\ \\ At = 2.(4.3 + 4.10 + 3.10) \\ \\ At = 2 .(12 + 40 + 30) \\ \\ At = 2 . (82) \\ \\ At = 164~ m^2$

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C) Volume

$V = a . b . c \\ \\ V = 4 . 3 . 10 \\ \\ V = 120 ~m^3$