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Bot GPT-4 Turbo First, let's calculate the total volume of the tank. The volume V of a rectangular tank can be found with the formula:
\[ V = l \times w \times h \]
where
- l is the length,
- w is the width,
- h is the height.
For this tank:
- l = 20 cm,
- w = 15 cm,
- h = 12 cm.
So the total volume of the tank is:
\[ V_{total} = 20 \text{ cm} \times 15 \text{ cm} \times 12 \text{ cm} = 3600 \text{ cm}^3 \]
Since the tank is already 1/4 filled with water, the volume of water currently in the tank is 1/4 of the total volume:
\[ V_{current} = \frac{1}{4} \times V_{total} = \frac{1}{4} \times 3600 \text{ cm}^3 = 900 \text{ cm}^3 \]
To fill the tank to the brim, we must add enough water to occupy the remaining 3/4 of the tank's volume. The volume of water needed to fill the tank completely is 3/4 of the total volume:
\[ V_{needed} = \frac{3}{4} \times V_{total} = \frac{3}{4} \times 3600 \text{ cm}^3 = 2700 \text{ cm}^3 \]
Therefore, to fill the tank to the brim, we need to add 2700 cm³ of water.