Question

The volume of a squared base cuboid is 675 cm³. If it's height is 3 cm, find it's length.

Answer 1

Recall that the volume of a squared base cuboid is:

$V=l^2\times h,$

where l is the length of the squared base, and h is the height of the cuboid.

Substituting V=675 cm³ and h=3cm we get:

$675cm^3=l^2\cdot3cm\text{.}$

Dividing the above result by 3cm we get:

$\begin{gathered} \frac{675cm^3}{3cm}=\frac{l^2\cdot3cm}{3cm}, \\ 225cm^2=l^2\text{.} \end{gathered}$

Therefore:

$\begin{gathered} l=\sqrt[]{225cm^2}, \\ l=15cm\text{.} \end{gathered}$

Answer: The length is 15cm.