Volume Word Problems - MathHelp.com - Geometry Help - Free Printable

To solve this problem, we need to find the volume of the fish based on how much the water level rises when the fish is placed in the aquarium.

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🔍 Given:

- The aquarium is a rectangular prism.
- Length = 75 cm
- Width = 35 cm
- Water level rises by 2 cm when the fish is added.
- The volume of water displaced by the fish equals the volume of the fish (by Archimedes' principle).

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🧮 Step-by-step Solution:

We use the formula for the volume of a rectangular prism:

$$
V = \text{Base Area} \times \text{Height}
$$

Here:
- Base Area = length × width = $75\, \text{cm} \times 35\, \text{cm}$
- Height = rise in water level = $2\, \text{cm}$

So,
$$
V_{\text{fish}} = 75 \times 35 \times 2
$$

First, calculate $75 \times 35$:
$$
75 \times 35 = (70 + 5) \times 35 = 70 \times 35 + 5 \times 35 = 2450 + 175 = 2625
$$

Now multiply by 2:
$$
2625 \times 2 = 5250
$$

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✔ Final Answer:

$$
\boxed{5250}\ \text{cm}^3
$$

The volume of the fish is 5250 cubic centimeters.

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💡 Explanation:

When the fish is placed in the aquarium, it displaces a volume of water equal to its own volume. The rise in water level forms a rectangular prism with the same base as the aquarium and height equal to the rise (2 cm). So, calculating that volume gives us the volume of the fish.

This is a classic application of displacement method to measure volume.