Name Class Date. How Much Lumber? Directions: Read the entire lab before doing the procedure and answering the questions.

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1 Inquiry Lab Outdoors Chapter 11 How Much Lumber? Directions: Read the entire lab before doing the procedure and answering the questions. Problem How can you calculate the amount of lumber in a tree? Background Using Triangles Foresters calculate the approximate amount of lumber in a tree, in order to ensure that they can obtain sufficient wood for commercial purposes. To make this estimate, they use two measurements the height of the tree, and the tree s diameter at breast height (DBH). The DBH is the diameter of the tree trunk at a distance of 4.5 feet from the ground. In this activity, you can estimate the height of the tree by using similar triangles. Board Feet These measurements will be used to calculate the volume of lumber in a tree. Foresters use the board foot as the unit of measurement. A board foot is 144 cubic inches and is often described as a board of wood that is one foot wide by one foot long by one inch thick (12 in. 12 in. 1 in. = 144 in. 3 ). Materials 12 inch rulers (2) 100 ft measuring tape masking tape calculator Safety Use safety goggles when holding a ruler near your eyes. Wash your hands with soap and water after you complete the activity. 1

2 Procedure Step 1 Choose a tree to measure. Face the tree and hold a ruler vertically in front of you. The distance from your eye to the ruler should equal one foot. CAUTION: Make sure you are wearing safety goggles. Hold a second ruler horizontally to check the distance. Keep the rulers in place for the next steps. Step 2 Step 3 Step 4 Step 5 Step 6 Close one eye and move toward or away from the tree until you can see the base of the trunk and the base of the vertical ruler in the same line of sight. Again, check the horizontal ruler to make sure the distance between the vertical ruler and your eye is still one foot. Keeping the base of the trunk and the bottom of the ruler in sight, move toward or away from the tree until the top of the ruler is in the same line of sight as the top of the tree. You may have to move the ruler up or down to do this. Place your pen or pencil on the ground to mark the spot where you were standing. Use the measuring tape to measure how far you were standing from the tree. This distance is the estimated height of the tree. Record the height in the data table. Using the measuring tape, measure the tree to a height of 4.5 feet from the bottom of the trunk. Use a small piece of masking tape to mark this height on the trunk. Repeat this process on the other side of the tree. To measure the circumference of the tree, use the masking tape marks as a guide. Wrap the measuring tape around the trunk of the tree at a height of 4.5 feet from the bottom of the trunk. Record the measurement in the data table. Remove the tape from the tree and clean up as directed by your teacher. Wash your hands thoroughly. 2

3 Build Math Skills To estimate the volume of usable lumber in a tree, estimate the number of board feet the trunk contains. Start with diameter at breast height (DBH). Use that to estimate the area of a circular cross-section, the volume of the trunk, and finally, the number of usable board feet. EXAMPLE A tree has a circumference of 65 in. at breast height of 4.5 ft. The tree s height is estimated to be 80 ft. Calculate the amount of the lumber in the tree. First Find the diameter at breast height (DBH) of the tree, in feet. Remember that the formula for the diameter (d) of a circle is circumference (C) divided by pi ( ). Use 3.14 for pi ( ). Use the diameter to find the radius. Use the formula radius equals one half the diameter: Convert the radius of the tree from inches to feet. Use the conversion factor ( 1 ft / 12 in.): Calculate the area of the circular cross-section of the tree at the height of 4.5 feet. Use the formula for the area of a circle: Calculate the volume of the tree trunk using the formula for the volume of a cylinder. Calculate the volume of a cylinder by multiplying the area of the circular cross section times the height: Finally Convert volume to board feet. Divide the trunk volume by 4, since only about one-fourth of the tree can be used to make boards: 192 ft 3 / 4 = 48 ft 3 Multiply the result by 12 since there are 12 board feet in a cubic foot: 48 ft 3 12 = 576 board feet 3

4 Observe and Collect Data 1. Record your data in the table. Data Table Estimated Height of Tree (ft) Circumference at 4.5 ft (in.) Use Questions 2 7 to calculate the usable volume of lumber in your tree, in board feet. 2. Find the diameter at breast height (DBH) of your tree, in inches. 3. Find the radius, in inches, based on the DBH. 4. Convert the radius from inches to feet. 5. Calculate the area of the circular cross-section (at the height of 4.5 ft). 6. Calculate the volume of your tree trunk using the formula for the volume of a cylinder. 7. Finally, convert the volume of your tree trunk to board feet. 4

5 Analyze and Conclude 8. Draw Conclusions During data collection, why did the distance from you to your tree equal the height of your tree? 9. Analyze Data Suppose it takes 6000 board feet of lumber to build a home with a floorplan of approximately 1100 ft 2. How many trees would be needed to build this house, if they are all the same size as the tree you measured? 10. Evaluate What are some possible sources of error in your measurements, calculations, and estamation in thi slab? How could you reduce errors if you were to repeat the activity? 11. Extension Research different certification agencies for forests, such as the Forest Stewardship Council (FSC) or the Sustainable Forestry Initiative (SFI). What standards must the timber industry meet in order to be certified? What do certifications from these agencies mean for the consumer? 5