A cylindrical tank of diameter 3.6 and height 2.5 internally is two thirds full of juice a) calculate the volume of the juice in litres ??

To calculate the volume of the juice in the cylindrical tank, we first need to find the volume of the entire tank and then multiply it by two thirds.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

Given that the diameter of the tank is 3.6, the radius (r) is half of the diameter, so r = 3.6/2 = 1.8.

The height (h) of the tank is 2.5.

Now, we can calculate the volume of the entire tank:
V = π(1.8)^2(2.5)
V = π(3.24)(2.5)
V = 25.5π

Since the tank is two thirds full of juice, we need to multiply the volume of the entire tank by two thirds:
Volume of juice = (2/3)(25.5π)
Volume of juice ≈ 16.9π

To convert this volume to litres, we can use the conversion factor 1 litre = 1000 cm^3:
Volume of juice ≈ 16.9π * 1000 cm^3
Volume of juice ≈ 16900π cm^3
Volume of juice ≈ 53060.3 cm^3

Therefore, the volume of the juice in the cylindrical tank is approximately 53060.3 cm^3 or 53.06 litres.

Step 1: Find the Volume of the Cylindrical Tank

The volume of a cylindrical tank is given by:

```
Volume = πr²h
```

where r is the radius and h is the height.

Given that the diameter is 3.6, the radius is:

```
r = 3.6 / 2 = 1.8 m
```

Given that the height is 2.5 m, the volume of the cylindrical tank is:

```
Volume = π(1.8)²(2.5) = 30.6 m³
```

Step 2: Find the Volume of the Juice

Since the tank is two thirds full, the volume of the juice is:

```
Volume of Juice = (2/3) - Volume of Tank
```

```
Volume of Juice = (2/3) - 30.6 m³
```

```
Volume of Juice = 20.4 m³
```

Step 3: Convert to Liters

1 cubic meter (m³) is equal to 1000 liters (L). Therefore, the volume of the juice in liters is:

```
Volume of Juice = 20.4 m³ × 1000 L/m³
```

```
Volume of Juice = 20,400 L
```

Therefore, the volume of the juice in the cylindrical tank is 20,400 liters.