A wooden cylinderical pole is 7 m high and its base radius is 10 cm. Find its weight if the wood weighs 225 kg per cubic metre.

Answer

To solve the problem of finding the weight of a wooden cylindrical pole, we will follow these steps:

### Step 1: Convert the radius from centimeters to meters
The radius of the base of the pole is given as 10 cm. To convert this to meters, we use the conversion factor:
1 cm = 0.01 m.

So,
\[ \text{Radius} = 10 \, \text{cm} = 10 \times 0.01 \, \text{m} = 0.1 \, \text{m}. \]

### Step 2: Identify the height of the pole
The height of the pole is given as 7 m.

### Step 3: Calculate the volume of the cylinder
The formula for the volume \( V \) of a cylinder is:
\[ V = \pi r^2 h, \]
where \( r \) is the radius and \( h \) is the height.

Substituting the values:
- \( r = 0.1 \, \text{m} \)
- \( h = 7 \, \text{m} \)

Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times (0.1)^2 \times 7. \]

Calculating \( (0.1)^2 \):
\[ (0.1)^2 = 0.01. \]

Now substituting back into the volume formula:
\[ V = \frac{22}{7} \times 0.01 \times 7. \]

The \( 7 \) in the numerator and denominator cancels out:
\[ V = 22 \times 0.01 = 0.22 \, \text{m}^3. \]

### Step 4: Calculate the weight of the wood
We know that the weight of the wood per cubic meter is 225 kg. To find the weight of the wooden pole, we multiply the volume by the weight per cubic meter:
\[ \text{Weight} = \text{Volume} \times \text{Weight per cubic meter} = 0.22 \, \text{m}^3 \times 225 \, \text{kg/m}^3. \]

Calculating the weight:
\[ \text{Weight} = 0.22 \times 225 = 49.5 \, \text{kg}. \]

### Final Answer
The weight of the wooden cylindrical pole is **49.5 kg**.

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