Me voy a comprar una barra de cortinas. Como vivo en un doceavo piso, me interesa saber cuál es la longitud máxima que puedo meter en el ascensor.
Así que saco mi cinta métrica de bolsillo, que sólo mide hasta un metro y mido el suelo que resulta ser un cuadrado de 1m x 1m, pero para la altura no da.
Eso sí, hay una pegatina en la caja del ascensor que dice que tiene una capacidad de 2500 litros.
Con toda esta información, ¿cuál es la longitud máxima de barra que me cabría en el ascensor?

So I take out my pocket tape measure, which only measures up to a meter and I measure the floor which turns out to be a square of 1m x 1m, but for the height it doesn't give.

However, there's a sticker on the lift box that says it has a capacity of 2,500 litres.

With all this information, what is the maximum length of bar that would fit me in the elevator?

step 1

Find the height of the elevator

we know that

The elevator has a capacity of 2,500 litres.

[tex]1\ m^3=1,000\ L[/tex]

so

[tex]2,500\ L=2.5\ m^3[/tex]

The volume of the elevator is given by

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the elevator

we have

[tex]B=(1)(1)=1\ m^2\\V=2.5\ m^3[/tex]

substitute

[tex]2.5=(1)h\\h=2.5\ m[/tex]

step 2

Find the diagonal of the base of the elevator

Let

d ---> diagonal of the base of the elevator

Applying the Pythagorean Theorem

[tex]d^2=b^2+b^2[/tex]

substitute

[tex]d^2=1^2+1^2[/tex]

[tex]d=\sqrt{2}\ m[/tex]

step 3

Find the diagonal of the rectangular prism (elevator)

Let

D ----> diagonal of the rectangular prism

d ---> diagonal of the base of elevator

h ----> height of the elevator

Applying the Pythagorean Theorem

[tex]D^2=d^2+h^2[/tex]

substitute

[tex]D^2=(\sqrt{2})^2+2.5^2[/tex]

[tex]D^2=8.25\\D=2.87\ cm[/tex]

therefore

The maximum length of the bar I could fit in the elevator is 2.87 meters.