An apartment complex has an in-ground pool that is in the shape of a cylinder with a diameter of 18 feet and a height of 5 feet. The pool is filled with water to a depth of 4.5 feet. If each person who enters the pool displaces about 2.5 cubic feet of water, approximately what maximum number of people will the pool hold without overflowing? Use 3.14 for pi and round to the nearest whole number of people.
To: oobleck
But what about the 4.5? Do we not need it?
uh, noooooo
the first 4.5 feet already are full of water
They just need to raise the water level the last 0.5 feet till it starts to overflow.
To find the maximum number of people the pool will hold without overflowing, we need to calculate the volume of the pool and then divide it by the volume of water displaced by each person.
1. Start by calculating the volume of the pool. The shape of the pool is a cylinder, so we can use the formula for the volume of a cylinder: V = π * r^2 * h, where V is the volume, π is approximately 3.14, r is the radius (half of the diameter), and h is the height of the cylinder.
Given that the diameter of the pool is 18 feet, the radius (r) is half of that, so r = 18/2 = 9 feet.
The height of the cylinder is 5 feet.
Now we can calculate the volume of the pool: V = 3.14 * 9^2 * 5.
V = 3.14 * 81 * 5.
V ≈ 1272.45 cubic feet.
2. Next, we need to find the volume of water displaced by each person. Given that each person displaces about 2.5 cubic feet of water, we already have this information.
3. Finally, we divide the volume of the pool by the volume of water displaced by each person to find the maximum number of people the pool will hold without overflowing.
Maximum number of people = Volume of the pool / Volume of water displaced by each person.
Maximum number of people ≈ 1272.45 / 2.5.
Maximum number of people ≈ 508.98.
Rounding to the nearest whole number, the maximum number of people the pool will hold without overflowing is approximately 509 people.
So, the pool will hold a maximum of approximately 509 people without overflowing.
so, you need .5 ft of height to be filled with people
v = pi * 9^2 * .5 ft^3
divide that by 2.5 to get the number of people