REFUERZO INTERNO “RESOLVEMOS DIVERSAS SITUACIONES COTIDIANAS UTILIZANDO PRISMAS”

A cuboid (rectoedro) has length $l$, width $w$, and height $h$. The space diagonal $d$ is given by the formula:

$$d = \sqrt{l^2 + w^2 + h^2}$$

From the image, we have:
$l = 4 \text{ m}$
$w = 2 \text{ m}$
$d = \sqrt{29} \text{ m}$

$$(\sqrt{29})^2 = (4)^2 + (2)^2 + h^2$$ $$29 = 16 + 4 + h^2$$ $$29 = 20 + h^2$$ $$h^2 = 29 - 20$$ $$h^2 = 9$$ $$h = \sqrt{9}$$ $$h = 3 \text{ m}$$

$$V = 4 \text{ m} \times 2 \text{ m} \times 3 \text{ m}$$ $$V = 24 \text{ m}^3$$

The volume of the cuboid is $\text{24 m}^3$.