The problem asks us to calculate the volume of water needed to fill a cuboid container, given the dimensions of the container and the height of the water already in it. We need to give the answer in $cm^3$. The dimensions are given in $mm$.

1. Problem Description

The problem asks us to calculate the volume of water needed to fill a cuboid container, given the dimensions of the container and the height of the water already in it. We need to give the answer in $cm^3$. The dimensions are given in $mm$.

2. Solution Steps

First, convert all dimensions from $mm$ to $cm$.

$1 cm = 10 mm$, so to convert from $mm$ to $cm$, divide by

1

0. Length = $115 mm = 11.5 cm$

Width = $80 mm = 8 cm$

Height of container = $525 mm = 52.5 cm$

Height of water = $450 mm = 45 cm$

Next, calculate the volume of the entire container.

Volume of cuboid = length × width × height

Volume of container = $11.5 cm \times 8 cm \times 52.5 cm = 4830 cm^3$

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

Volume of water = $11.5 cm \times 8 cm \times 45 cm = 4140 cm^3$

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

Volume of water needed = Volume of container - Volume of water

Volume of water needed = $4830 cm^3 - 4140 cm^3 = 690 cm^3$

3. Final Answer

$690$