Gopal filled a fish tank measuring 84 cm by 50 cm by 40 cm with water. What was the volume of the water measuring when it was 2 3 full?
To find the volume of water when the fish tank is \( \frac{2}{3} \) full, we first need to calculate the tank's total volume and then take two-thirds of that volume.
The volume \( V \) of a rectangular tank can be found with the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given the tank's dimensions:
Length \( l = 84 \) cm
Width \( w = 50 \) cm
Height \( h = 40 \) cm
The total volume of the tank \( V_{\text{total}} \) is:
\[ V_{\text{total}} = 84 \text{ cm} \times 50 \text{ cm} \times 40 \text{ cm} \]
\[ V_{\text{total}} = 168000 \text{ cm}^3 \]
Now that we have the total volume, we can find the volume when the tank is \( \frac{2}{3} \) full by multiplying the total volume by \( \frac{2}{3} \):
\[ V_{\frac{2}{3} \text{full}} = \frac{2}{3} \times V_{\text{total}} \]
\[ V_{\frac{2}{3} \text{full}} = \frac{2}{3} \times 168000 \text{ cm}^3 \]
\[ V_{\frac{2}{3} \text{full}} = 112000 \text{ cm}^3 \]
So, the volume of the water when the tank is \( \frac{2}{3} \) full is 112,000 cubic centimeters, or 112 liters, since 1,000 cubic centimeters is equivalent to 1 liter.