Question

What is the volume of the box with a square base

Answer 1

We must find the volume of a box with:

• square base with diagonal ,h = 6 cm,,

,

• height ,H = 15 cm,.

1) First we compute the length of the sides of the square base.

From the diagram above, we see that the diagonal of the box constitutes the hypotenuse of a triangle of sides a. Pitagoras Theorem states that the square of the hypotenuse is equal to the sum of the squares of the other sides, so we have:

$h^2=a^2+a^2=2a^2\text{.}$

Replacing the value h = 6 cm, and solving for a², we get:

$\begin{gathered} (6\operatorname{cm})^2=2a^2, \\ 36cm^2=2a^2, \\ a^2=\frac{36cm^2}{2}, \\ a^2=18cm^2\text{.} \end{gathered}$

2) The volume is given by the product of height (H) and the area of the base (a²):

$V=H\cdot a^2=15\operatorname{cm}\cdot18cm^2=270cm^3.$

Answer

The volume of the box is 270 cm³.