The problem asks for the volume of water needed to fill a cuboid container, given its dimensions and the height of the water currently in the container. The dimensions are: width = 115 mm, length = 80 mm, and height of the container = 525 mm. The current water height is 450 mm. The final answer should be in $cm^3$.

1. Problem Description

The problem asks for the volume of water needed to fill a cuboid container, given its dimensions and the height of the water currently in the container. The dimensions are: width = 115 mm, length = 80 mm, and height of the container = 525 mm. The current water height is 450 mm. The final answer should be in $cm^3$.

2. Solution Steps

First, we need to calculate the volume of the entire container.

$Volume_{container} = width \times length \times height$

$Volume_{container} = 115 \times 80 \times 525$

$Volume_{container} = 483000 \, mm^3$

Next, calculate the volume of the water currently in the container.

$Volume_{water} = width \times length \times water\,height$

$Volume_{water} = 115 \times 80 \times 450$

$Volume_{water} = 414000 \, mm^3$

Now, calculate the volume of water needed to fill the container.

$Volume_{needed} = Volume_{container} - Volume_{water}$

$Volume_{needed} = 483000 - 414000$

$Volume_{needed} = 69000 \, mm^3$

Finally, convert the volume from $mm^3$ to $cm^3$. Since $1\,cm = 10\,mm$, then $1\,cm^3 = (10\,mm)^3 = 1000\,mm^3$.

$Volume_{needed} \, (cm^3) = \frac{Volume_{needed} \, (mm^3)}{1000}$

$Volume_{needed} \, (cm^3) = \frac{69000}{1000}$

$Volume_{needed} \, (cm^3) = 69 \, cm^3$

3. Final Answer

$69$