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?

Use feet for measurements.

Diameter, D = 8
Length, L = 8
Volume, V = (L/4)πD²
Volume of cartons, v, one per victim
= (6/12)*(6/12)*(12/12)
= 1/4 cubic foot
Number of victims served, N
= V/v, round down to the nearest whole number

To find out how many victims will get a full container of water, we need to compare the volume of the cylindrical tank with the volume of a carton.

First, let's calculate the volume of the cylindrical tank:
The formula to calculate the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

Given that the diameter of the tank is 8 ft, we can calculate the radius by dividing the diameter by 2:
radius = diameter/2 = 8 ft / 2 = 4 ft

And the height of the tank is also 8 ft.

Plugging these values into the formula, we get:
V_tank = π(4 ft)^2(8 ft)
V_tank = π(16 ft^2)(8 ft)
V_tank = π(128 ft^3)
V_tank ≈ 402.12 ft^3

Now, let's calculate the volume of the carton:
The volume of a rectangular prism (carton) is given by V = lwh, where l is the length, w is the width, and h is the height.

Given that the dimensions of the carton are 6 in. × 6 in. × 12 in., we convert them to feet by dividing each dimension by 12:
length = 6 in. / 12 = 0.5 ft
width = 6 in. / 12 = 0.5 ft
height = 12 in. / 12 = 1 ft

Plugging these values into the formula, we get:
V_carton = (0.5 ft)(0.5 ft)(1 ft)
V_carton = 0.25 ft^3

Finally, we can calculate the number of victims who will get a full container of water by dividing the volume of the tank by the volume of a carton:
Number of victims = V_tank / V_carton
Number of victims ≈ 402.12 ft^3 / 0.25 ft^3
Number of victims ≈ 1608.48

Therefore, approximately 1608 victims will get a full container of water.