Final answer:
The correct formula to find the volume of the cone-shaped popcorn container with a diameter of 10 inches and a height of 18 inches is V = (1/3) × π × 10^2 × 18. This formula applies the volume of a cone equation by halving the diameter to get the radius.
Step-by-step explanation:
The popcorn containers are in the shape of cones, and we are given that the container has a diameter of 10 inches and a height of 18 inches. We are required to write an equation and solve for the volume of the container. To do this, we use the formula for the volume of a cone, which is V = (1/3) × π × r^2 × h, where r is the radius (half of the diameter), and h is the height.
Since the diameter is 10 inches, the radius (r) will be half of that, which is 5 inches. Plugging the values into the formula gives us:
V = (1/3) × π × (5 inches)^2 × 18 inches
V = (1/3) × π × 25 in^2 × 18 in
V = (1/3) × π × 450 in^3
V = 150 π in^3
So, the correct equation to use to determine the volume of the popcorn container is option A: V = (1/3) × π × 10^2 × 18.