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* 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} (675cm^3)/(3cm)=(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.