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Let's break down the problem step by step:

### Given:
- The tank has a **length** of 36 cm, a **breadth** of 30 cm, and initially contains water up to a **height** of 20 cm.
- Water is used from the tank to fill **twelve ¾-liter containers**.
- After removing the water, the tank is **⅓ full**.

### Required:
- **(a)** The capacity of the tank.
- **(b)** The full height of the tank.

### Step 1: Calculate the initial volume of water in the tank.
The volume of a rectangular tank is given by the formula:

\[
\text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height}
\]

Here:
- Length = 36 cm,
- Breadth = 30 cm,
- Height = 20 cm.

\[
\text{Initial Volume} = 36 \times 30 \times 20 = 21,600 \, \text{cm}^3
\]

Since \(1 \, \text{cm}^3 = 1 \, \text{mL}\), this is equivalent to **21.6 liters**.

### Step 2: Calculate the total volume of water used to fill the containers.
Each container holds \( \frac{3}{4} \) liters, and there are 12 containers. So, the total volume of water used is:

\[
\text{Water used} = 12 \times \frac{3}{4} = 9 \, \text{liters}
\]

### Step 3: Calculate the remaining water in the tank after removing the water.
The initial water in the tank was 21.6 liters, and 9 liters were removed. Therefore, the remaining water in the tank is:

\[
\text{Remaining water} = 21.6 - 9 = 12.6 \, \text{liters}
\]

### Step 4: Determine the capacity of the tank.
After removing the water, the tank is \( \frac{1}{3} \) full, and the remaining water is 12.6 liters. Therefore, the full capacity of the tank is:

\[
\frac{1}{3} \times \text{Full Capacity} = 12.6
\]

\[
\text{Full Capacity} = 12.6 \times 3 = 37.8 \, \text{liters}
\]

### Step 5: Determine the height of the tank.
The capacity of the tank is related to its dimensions by the formula:

\[
\text{Capacity} = \text{Length} \times \text{Breadth} \times \text{Height}
\]

The length and breadth are given as 36 cm and 30 cm, and we have already calculated the full capacity to be 37.8 liters (which is 37,800 cm³). Therefore, we can solve for the height:

\[
37,800 = 36 \times 30 \times \text{Height}
\]

\[
\text{Height} = \frac{37,800}{36 \times 30} = \frac{37,800}{1,080} = 35 \, \text{cm}
\]

### Final Answers:
- **(a)** The capacity of the tank is **37.8 liters**.
- **(b)** The height of the tank is **35 cm**.

Would you like further details on any of these steps?

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Here are 5 related questions for further exploration:
1. How would the problem change if the containers held 1 liter each?
2. What is the volume of the tank in cubic meters?
3. If the tank were half full instead of one-third, how much water would it contain?
4. How much water would need to be added to fill the tank completely?
5. What would be the effect on the tank's capacity if the dimensions were doubled?

**Tip:** When dealing with problems involving volume, remember that volume measurements can be converted between units like liters and cubic centimeters, which is especially useful for water-related problems.

A rectangular tank, of length 36 cm and breadth 30 cm, contained water up to a height of 20 cm. Some water from the tank was used to fill twelve 3/4 liter containers. The tank then became 1/3 full. Find (a) the capacity of the tank, (b) the height of the tank.

Solve a rectangular tank volume problem where water is used to fill containers and the tank becomes partially full. Learn how to calculate the capacity of the tank and determine its full height. Step-by-step solution suitable for Grades 6-8.

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