A water delivery truck with a cylindrical tank measuring 8 ft in diameter and 8 ft long dispenses
water to drought victims in cartons measuring 6 in. × 6 in. × 12 in. How many victims will get a full
container of water?
each box has a volume of
(.5)(.5)(1) cubic feet
= .25 cubic feet
the water tank has a volume of
pi(4^2)(8) cubic feet
= 402.1239 cubic feet
how many times does .25 go into 402.1239 ?
402.1239 ÷ .25 = 1608.5
so 1608 victims will get a full container.
To find out how many victims will get a full container of water, we need to determine the volume of water that can be carried by the truck and the volume of water that can fit into one carton.
1. Calculate the volume of the cylindrical tank:
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Since the diameter of the tank is 8 ft, the radius (r) is half of that, which is 4 ft.
Therefore, the volume of the cylindrical tank is V = π(4 ft)^2(8 ft) = 128π ft^3.
2. Convert the volume of the tank to cubic inches:
Since the cartons' dimensions are given in inches, we need to convert the volume of the tank to cubic inches. Since 1 ft = 12 inches, 1 ft^3 = (12 inches)^3 = 1728 in^3.
Therefore, the volume of the cylindrical tank in cubic inches is 128π ft^3 * 1728 in^3/ft^3 = 221184π in^3.
3. Calculate the volume of one carton:
The volume of one carton is V = length × width × height = 6 in × 6 in × 12 in = 432 in^3.
4. Determine the number of victims that will get a full container of water:
Divide the volume of the tank by the volume of one carton: 221184π in^3 / 432 in^3 ≈ 512π ≈ 1609 victims.
Therefore, approximately 1609 victims will get a full container of water from the truck.
To determine how many victims will get a full container of water, we first need to calculate the volume of the truck tank and the volume of each carton. Then we can divide the tank's volume by the carton's volume to find the number of full cartons that can be filled.
Step 1: Calculate the volume of the truck tank
The truck tank is a cylinder, and the volume of a cylinder can be calculated using the formula:
Volume = π * radius^2 * height
Given that the tank has a diameter of 8 ft, the radius (r) is half the diameter, so r = 8 ft / 2 = 4 ft.
The height (h) of the tank is also 8 ft.
Using the formula, we can calculate the volume of the truck tank:
Volume = π * 4 ft^2 * 8 ft = 128π ft^3 (approximately 402.1 ft^3)
Step 2: Calculate the volume of each carton
The volume of a rectangular box (carton) can be calculated by multiplying its length, width, and height.
Given that the dimensions of the carton are 6 in. × 6 in. × 12 in., we need to convert them to the same unit as the tank (feet) before calculating the volume.
1 foot = 12 inches, so each dimension in feet is:
Length = 6 in. / 12 = 0.5 ft
Width = 6 in. / 12 = 0.5 ft
Height = 12 in. / 12 = 1 ft
Using these dimensions, we can calculate the volume of each carton:
Volume = 0.5 ft * 0.5 ft * 1 ft = 0.25 ft^3
Step 3: Calculate the number of victims who will get a full container
To find the number of full cartons that can be filled, we divide the tank's volume by the carton's volume:
Number of full cartons = Volume of truck tank / Volume of each carton
Number of full cartons = 128π ft^3 / 0.25 ft^3 ≈ 512π
Therefore, approximately 512π or 1609 people will get a full container of water.