A rectangular tank 27 cm by 18 cm by 39 cm is half filled with water.The water is poured into a cubical tank of edge 15 cm until it is 2/3 full.How much water is left in the rectangular tank?Give your answer in Litres.

To solve this problem, we'll need to calculate the volume of water initially in the rectangular tank, determine how much water is poured into the cubical tank, and then find out how much water is left in the rectangular tank.

### Step 1: Calculate the total volume of the rectangular tank in cubic centimeters (cm³).
The dimensions of the rectangular tank are:
- Length = 27 cm
- Width = 18 cm
- Height = 39 cm

The total volume \( V \) of the rectangular tank is given by:
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
\[
V = 27 \, \text{cm} \times 18 \, \text{cm} \times 39 \, \text{cm}
\]
\[
V = 18,954 \, \text{cm}^3
\]

### Step 2: Calculate the initial volume of water in the rectangular tank.
Since the tank is half filled with water, the volume of water in the rectangular tank is:
\[
\text{Volume of Water} = \frac{1}{2} \times 18,954 \, \text{cm}^3
\]
\[
\text{Volume of Water} = 9,477 \, \text{cm}^3
\]

### Step 3: Calculate the volume of water needed to fill the cubical tank 2/3 full.
The edge of the cubical tank is 15 cm, so the total volume \( V \) of the cubical tank is:
\[
V = \text{Edge}^3
\]
\[
V = 15 \, \text{cm} \times 15 \, \text{cm} \times 15 \, \text{cm}
\]
\[
V = 3,375 \, \text{cm}^3
\]
To fill the cubical tank 2/3 full:
\[
\text{Volume of Water} = \frac{2}{3} \times 3,375 \, \text{cm}^3
\]
\[
\text{Volume of Water} = 2,250 \, \text{cm}^3
\]

### Step 4: Calculate the remaining volume of water in the rectangular tank.
The initial volume of water in the rectangular tank was 9,477 cm³. After pouring 2,250 cm³ into the cubical tank, the remaining volume of water is:
\[
\text{Remaining Volume of Water} = 9,477 \, \text{cm}^3 - 2,250 \, \text{cm}^3
\]
\[
\text{Remaining Volume of Water} = 7,227 \, \text{cm}^3
\]

### Step 5: Convert the remaining volume of water to liters.
Since 1 liter is equal to 1,000 cubic centimeters:
\[
\text{Remaining Volume of Water in Liters} = \frac{7,227 \, \text{cm}^3}{1,000}
\]
\[
\text{Remaining Volume of Water in Liters} = 7.227 \, \text{L}
\]

### Final Answer:
The amount of water left in the rectangular tank is **7.227 liters**.

Would you like further details or have any other questions?

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Here are 5 related questions you might find helpful:
1. How do you calculate the volume of a triangular prism-shaped tank?
2. What would happen if the cubical tank were completely filled instead of 2/3 full?
3. How much water would overflow if more water were added to the cubical tank?
4. How do you convert between milliliters and liters when dealing with small tanks?
5. How would the answer change if the rectangular tank were filled to a different fraction?

**Tip:** When dealing with cubic tanks, remember that all sides are equal, which simplifies volume calculations significantly.

Learn how to calculate the remaining water in a rectangular tank and a cubical tank using volume calculations and unit conversions. This problem involves finding the initial volume of water in the rectangular tank, pouring water into a cubical tank, and determining the remaining volume in liters. Suitable for Grades 7-9.

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