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

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)