Trees that are cut down and stripped of their branches for timber are approximately cylindrical. A timber company specializes in a certain type of tree that has a typical diameter of 50 cm and a typical height of about 10 meters. The density of the wood is 380 kilograms per cubic meter, and the wood can be sold by mass at a rate of $4.75 per kilogram. What is the minimum number of whole trees that must be sold to raise at least $50,000?

Question

Mathematics

Elise Adams

19 July, 07:08

Trees that are cut down and stripped of their branches for timber are approximately cylindrical. A timber company specializes in a certain type of tree that has a typical diameter of 50 cm and a typical height of about 10 meters. The density of the wood is 380 kilograms per cubic meter, and the wood can be sold by mass at a rate of $4.75 per kilogram. What is the minimum number of whole trees that must be sold to raise at least $50,000?

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Answers (1)

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Houston Andrews · Answer 1

Given:

d = 50cm = 0.05m

h = 10 m

density = 380 kg/m³

rate of each tree = $4.75/kg

Required:

How many cylindrical trees must be sold to raise $50,000?

Solution:

We need to calculate first the average volume of the trees. We can calculate it by:

Volume = Area of circle x height

Volume = πd²/4 * h

Volume = π (0.05m) ²/4 * 10m

Volume = 0.0196 m³

Next, we calculate the weight of each tree by:

Mass = Density * Volume

Mass = 380kg/m³ * 0.0196m³

Mass = 7.46kg

We then calculate the price of each tree by:

Price = rate of each tree * mass

Price = $4.75/kg * 7.46kg

Price = $35.44

Lastly, to calculate how many trees, we can:

No. of trees = $50,000/$35.44

No. of trees = 1410.79 ≈ 1411 trees