Answer:
14.0 mm (1 d.p.)
Step-by-step explanation:
The volume of a cuboid is the product of its width, length and height:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Cuboid}}\\\\V=w \times l \times h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$w$ is the width of the base.}\\\phantom{ww}\bullet\;\textsf{$l$ is the length of the base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]
Therefore, to find the length of a cuboid, given its width and height, we simply substitute the given values into the formula and solve for length.
In this case:
- V = 3234 mm³
- w = 7 mm
- h = 33 mm
Substitute the values into the formula:
[tex]3234\; \textsf{mm$^3$}=7\; \textsf{mm} \times l \times 33\; \textsf{mm}[/tex]
Simplify the right side of the equation:
[tex]3234\; \textsf{mm$^3$}=231\;\textsf{mm$^2$} \times l[/tex]
Isolate [tex]l[/tex] by dividing both sides of the equation by 231 mm²:
[tex]l=\dfrac{3234\; \textsf{mm$^3$}}{231\;\textsf{mm$^2$}}[/tex]
Simplify:
[tex]l=14\; \sf mm[/tex]
Therefore, the length of the cuboid is exactly 14 mm, which is 14.0 mm to one decimal place.
