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Answer :
To find the volume of the timber that can be obtained from the cylindrical trunk of a tree, we need to follow these steps:
1. Understand the Problem:
- We know the circumference of the trunk is 176 cm.
- The length of the trunk (or height of the cylinder) is 2 meters, which is 200 centimeters (since 1 meter = 100 centimeters).
2. Find the Radius of the Cylinder:
- The formula for the circumference of a circle is:
[tex]\[
\text{Circumference} = 2 \times \pi \times \text{radius}
\][/tex]
- We can rearrange this formula to solve for the radius:
[tex]\[
\text{radius} = \frac{\text{Circumference}}{2 \times \pi}
\][/tex]
- Plug in the values:
[tex]\[
\text{radius} = \frac{176}{2 \times 3.14} \approx 28.025 \, \text{cm}
\][/tex]
3. Calculate the Volume of the Cylinder:
- The formula for the volume of a cylinder is:
[tex]\[
\text{Volume} = \pi \times \text{radius}^2 \times \text{height}
\][/tex]
- Using the radius we found and the given height:
[tex]\[
\text{Volume} = 3.14 \times (28.025)^2 \times 200
\][/tex]
4. Final Answer:
- The volume of the timber is approximately 493,248.41 cubic centimeters.
This is the volume of the timber obtained from the trunk, taking into account the dimensions and the given value of [tex]\(\pi\)[/tex].
1. Understand the Problem:
- We know the circumference of the trunk is 176 cm.
- The length of the trunk (or height of the cylinder) is 2 meters, which is 200 centimeters (since 1 meter = 100 centimeters).
2. Find the Radius of the Cylinder:
- The formula for the circumference of a circle is:
[tex]\[
\text{Circumference} = 2 \times \pi \times \text{radius}
\][/tex]
- We can rearrange this formula to solve for the radius:
[tex]\[
\text{radius} = \frac{\text{Circumference}}{2 \times \pi}
\][/tex]
- Plug in the values:
[tex]\[
\text{radius} = \frac{176}{2 \times 3.14} \approx 28.025 \, \text{cm}
\][/tex]
3. Calculate the Volume of the Cylinder:
- The formula for the volume of a cylinder is:
[tex]\[
\text{Volume} = \pi \times \text{radius}^2 \times \text{height}
\][/tex]
- Using the radius we found and the given height:
[tex]\[
\text{Volume} = 3.14 \times (28.025)^2 \times 200
\][/tex]
4. Final Answer:
- The volume of the timber is approximately 493,248.41 cubic centimeters.
This is the volume of the timber obtained from the trunk, taking into account the dimensions and the given value of [tex]\(\pi\)[/tex].
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