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?
Bring everything to feet as a unit, so the cartons are
.5 * .5 * 1 cu. ft. = 0.25 cu.ft.
For the tank, it's pi r^2 h again:
pi * 16 * 8
= 128 pi cu. ft.
So how many containers will that fill?
To determine the number of victims that will get a full container of water, we need to calculate the volume of the water tank and the volume of each carton, and then divide the volume of the tank by the volume of a single carton.
First, let's calculate the volume of the water tank. Given that it is a cylinder with a diameter of 8 ft and a length of 8 ft, we can use the formula for the volume of a cylinder:
Volume of cylinder = π * (radius)^2 * height
The diameter is 8 ft, so the radius is half of that, which is 4 ft. The height is also 8 ft. Let's substitute these values into the formula:
Volume of cylinder = π * (4 ft)^2 * 8 ft
= π * 16 ft^2 * 8 ft
= 128π ft^3
So, the volume of the water tank is 128π cubic feet.
Now, let's calculate the volume of each carton. The dimensions are given as 6 in. × 6 in. × 12 in. To find the volume, we multiply these three dimensions:
Volume of carton = 6 in. * 6 in. * 12 in.
= 432 in^3
But we need to convert the volume to cubic feet to match the units of the tank.
1 cubic foot = 12 in. * 12 in. * 12 in.
= 1728 in^3
So, the volume of the carton in cubic feet is:
Volume of carton = 432 in^3 / 1728 in^3 per cubic foot
= 0.25 ft^3
Finally, we can determine the number of victims that will get a full container of water by dividing the volume of the tank by the volume of each carton:
Number of victims = Volume of tank / Volume of carton
= 128π ft^3 / 0.25 ft^3
≈ 512π
Therefore, approximately 512π victims will get a full container of water.