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?

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