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23 December, 18:29

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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  1. 23 December, 18:43
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    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
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