the main trunk of a tree is in the shape of a cylinder. The distance around its cross section is 47.1cm and its height is 0.7m. What is the radius of the cross section? I know i have the height and circumference, would i divide the circumference by 4 to get the radius? how would i show my work? plz help! thx.
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To find the radius of the cross section of the tree trunk, you need to divide the circumference of the cross section by 2π (twice the value of pi).
First, let's write down the information given:
- The circumference of the cross section is 47.1 cm.
- The height of the cylinder (tree trunk) is 0.7 m.
Now let's find the radius step-by-step:
1. Convert the height of the tree trunk from meters to centimeters:
height (cm) = height (m) × 100
height (cm) = 0.7 m × 100 = 70 cm
2. Divide the circumference by 2π to find the radius:
radius = circumference / (2π)
radius = 47.1 cm / (2 × π)
radius ≈ 7.5 cm
Therefore, the radius of the cross section of the tree trunk is approximately 7.5 cm.
To find the radius of the cross section, you need to divide the circumference by 2π (twice the value of pi). Dividing the circumference by 4 would not give you the correct radius.
Here's how you can solve this problem step by step:
1. Given data:
- Circumference = 47.1 cm
- Height = 0.7 m
2. Convert the height to centimeters to match the units:
- 1 m = 100 cm (multiply the height by 100)
- Height = 0.7 m * 100 cm/m = 70 cm
3. The formula to find the circumference of a cylinder is: C = 2πr, where C is the circumference and r is the radius.
4. Rearrange the formula to solve for the radius:
- r = C / (2π)
5. Substitute the given circumference into the formula:
- r = 47.1 cm / (2π)
6. Calculate the value:
- r ≈ 47.1 cm / (2 * 3.14159)
- r ≈ 7.5 cm
So, the radius of the cross section of the trunk is approximately 7.5 cm.
The radius has nothing to do with the height. It equals (circumference)/(2 pi)
What they call the "distance around the cross section" is the circumference