A petrol tank is a cylinder of base diameter 28cm and length 24cm filted with conical ends each of axis length 9cm. Determine the capacity of the tank.

Answer

To determine the capacity of the petrol tank, we need to calculate the volume of the cylindrical part and the volume of the two conical ends, then sum these volumes.

### Step 1: Calculate the radius of the cylinder
The diameter of the cylinder is given as 28 cm. The radius (r) is half of the diameter.

\[ r = \frac{diameter}{2} = \frac{28 \, \text{cm}}{2} = 14 \, \text{cm} \]

**Hint:** Remember that the radius is always half of the diameter.

### Step 2: Calculate the volume of the cylindrical part
The formula for the volume (V) of a cylinder is given by:

\[ V = \pi r^2 h \]

Where:
- \( r \) is the radius,
- \( h \) is the height of the cylinder.

Given that the height of the cylinder is 24 cm, we can substitute the values into the formula:

\[ V_{cylinder} = \pi \times (14 \, \text{cm})^2 \times 24 \, \text{cm } \]

Using \( \pi \approx \frac{22}{7} \):

\[ V_{cylinder} = \frac{22}{7} \times 14^2 \times 24 \]

Calculating \( 14^2 = 196 \):

\[ V_{cylinder} = \frac{22}{7} \times 196 \times 24 \]

Now, simplify:

\[ = \frac{22 \times 196 \times 24}{7} \]

Calculating \( \frac{196}{7} = 28 \):

\[ = 22 \times 28 \times 24 \]

Calculating \( 22 \times 28 = 616 \):

\[ = 616 \times 24 = 14784 \, \text{cm}^3 \]

### Step 3: Calculate the volume of the conical ends
The formula for the volume of a cone is given by:

\[ V = \frac{1}{3} \pi r^2 h \]

Here, the radius of the cone is the same as the cylinder (14 cm) and the height of each cone is 9 cm. Since there are two cones, we will multiply the volume of one cone by 2.

\[ V_{cone} = 2 \times \left(\frac{1}{3} \pi r^2 h\right) \]

Substituting the values:

\[ V_{cone} = 2 \times \frac{1}{3} \times \frac{22}{7} \times (14 \, \text{cm})^2 \times 9 \, \text{cm} \]

Calculating \( 14^2 = 196 \):

\[ V_{cone} = 2 \times \frac{1}{3} \times \frac{22}{7} \times 196 \times 9 \]

Calculating \( \frac{196}{3} = 65.33 \):

\[ = 2 \times \frac{22 \times 65.33 \times 9}{7} \]

Calculating \( 22 \times 65.33 = 1437.26 \):

\[ = \frac{2 \times 1437.26 \times 9}{7} \]

Calculating \( 1437.26 \times 9 = 12935.34 \):

\[ = \frac{2 \times 12935.34}{7} \]

Calculating \( \frac{12935.34}{7} = 1847.91 \):

\[ = 2 \times 1847.91 = 3695.82 \, \text{cm}^3 \]

### Step 4: Calculate the total volume
Now, we can find the total volume of the petrol tank by adding the volume of the cylinder and the volume of the two cones.

\[ V_{total} = V_{cylinder} + V_{cone} \]

Substituting the values:

\[ V_{total} = 14784 \, \text{cm}^3 + 3695.82 \, \text{cm}^3 \]

Calculating:

\[ V_{total} = 18479.82 \, \text{cm}^3 \]

### Final Answer
The capacity of the petrol tank is approximately \( 18480 \, \text{cm}^3 \).

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