A company is designing a new packaging container for their product. They want to create a cone-shaped container with a height of 8 inches and a base diameter of 6 inches. The container will be made of a special material that costs $0.10 per cubic inch.
What is the volume of the container?
What is the slant height of the container?
What is the total cost of the material used in the container?
To solve this problem, we need to first find the volume of the cone. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. Since we are given the diameter of the base, we need to divide it by 2 to get the radius.
r = 6/2 = 3 inches
h = 8 inches
V = (1/3)π(3²)(8) = 24π cubic inches
Next, we need to find the slant height of the cone. The formula for the slant height of a cone is L = √(r² + h²).
L = √(3² + 8²) = √(9 + 64) = √73 ≈ 8.54 inches
Finally, we can calculate the total cost of the material used in the container by multiplying the volume of the cone by the cost per cubic inch.
Total cost = 24π x $0.10 = $2.40π ≈ $7.54
Therefore, the volume of the container is 24π cubic inches, the slant height of the container is √73 inches, and the total cost of the material used in the container is approximately $7.54.