a movie theater Is considering two different sized containers for its popcorn. One option is a cone shaped cup that has a diameter of 10 cm and a height of 6 cm. The other option is a cylinder that has a diameter of 8 cm and a height of 12 cm. what container holds more?
The cylinder one.
Vcylinder = pi*r^2*h = pi * 4^2 *12 = 192*pi cm^3
Vcone = 1/3 * pi * r^2 * h = 1/3 * pi * 5^2 * 6 = 50*pi cm^3
To determine which container holds more popcorn, we need to compare their volumes.
Let's start with the cone-shaped cup. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height. Given that the diameter of the cone is 10 cm, the radius is half of the diameter, so r = 10/2 = 5 cm. Substituting these values into the formula, we get V_cone = (1/3)π(5²)(6).
Next, let's calculate the volume of the cylinder. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Given that the diameter of the cylinder is 8 cm, the radius is half of the diameter, so r = 8/2 = 4 cm. Substituting these values into the formula, we get V_cylinder = π(4²)(12).
Now, we can calculate the volumes of both containers:
V_cone = (1/3)π(5²)(6)
V_cone ≈ 157.08 cm³
V_cylinder = π(4²)(12)
V_cylinder ≈ 603.19 cm³
Comparing the volumes, we can see that the cylinder holds more popcorn with a volume of approximately 603.19 cm³, while the cone-shaped cup holds approximately 157.08 cm³. Therefore, the cylinder is the container that holds more popcorn.