A raft is made of 15 logs lashed together. Each is 30.0 cm in diameter and has a length of 7.00 m. How many people (whole number) can the raft hold before they start getting their feet wet, assuming the average person has a mass of 66.0 kg? Do not neglect the weight of the logs. Assume the density of wood is 600 kg/m³.

I tried it two different ways and got 45 and 50 but both answers are incorrect

To solve this problem, we need to determine the total weight the raft can support before it starts sinking.

First, let's calculate the weight of each log:
Density of wood = 600 kg/m³
Volume of each log = π(r^2)h = π(0.15m/2)^2 * 7m = 0.14875 m³
Mass of each log = Density * Volume = 600 kg/m³ * 0.14875 m³ = 89.25 kg

Next, let's calculate the total weight of all the logs:
Number of logs = 15
Total weight of logs = Mass of each log * Number of logs = 89.25 kg * 15 = 1338.75 kg

To determine the number of people the raft can hold, we need to consider the weight of the people as well. Each person has a mass of 66.0 kg.

Weight of the raft + weight of people = Total weight the raft can support

Let's assume the raft can support the weight without sinking, but it should not exceed the maximum weight it can hold.

Let's say x is the number of people the raft can hold:
Total weight of the raft + weight of people = Total weight the raft can support

1338.75 kg + 66.0 kg * x <= maximum total weight

Here, maximum total weight is the weight the raft can support without sinking, and we need to solve for x.

Now, let's solve for x:
1338.75 kg + 66.0 kg * x ≤ maximum total weight

To determine the maximum total weight, we need to consider Archimedes' principle, which states that the weight of the displaced water is equal to the weight of the object.

Volume of displaced water = Volume of each log * Number of logs
= 0.14875 m³ * 15 = 2.23125 m³
Weight of displaced water = Volume of displaced water * Density of water (1000 kg/m³)
= 2.23125 m³ * 1000 kg/m³ = 2231.25 kg

Therefore, the maximum total weight the raft can support is 2231.25 kg.

Now let's solve for x in the inequality:

1338.75 kg + 66.0 kg * x ≤ 2231.25 kg

Rearranging the equation:

66.0 kg * x ≤ 2231.25 kg - 1338.75 kg
66.0 kg * x ≤ 892.5 kg
x ≤ 892.5 kg / 66.0 kg
x ≤ 13.5

Since we cannot have a fraction of a person, the maximum number of people the raft can hold is 13.

Therefore, the raft can hold a maximum of 13 people before their feet start getting wet.