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?
compare the volumes:
cone: pi/3 * 5^2 * 6
cylinder: pi * 4^2 * 12
To determine which container holds more popcorn, we need to calculate the volume of each container and compare the values.
Let's start with the cone-shaped cup. The formula to calculate the volume of a cone is V = (1/3) * π * r^2 * h, where V is the volume, π is a constant approximately equal to 3.14, r is the radius of the base (half of the diameter), and h is the height.
For the cone-shaped cup:
- Diameter = 10 cm, so the radius (r) = 5 cm.
- Height (h) = 6 cm.
Plugging the values into the formula:
V = (1/3) * 3.14 * 5^2 * 6
= (1/3) * 3.14 * 25 * 6
≈ 31.4 * 25 * 6
≈ 4710 cubic cm
Now let's calculate the volume of the cylinder. The formula for the volume of a cylinder is V = π * r^2 * h.
For the cylinder:
- Diameter = 8 cm, so the radius (r) = 4 cm.
- Height (h) = 12 cm.
Plugging the values into the formula:
V = 3.14 * 4^2 * 12
= 3.14 * 16 * 12
≈ 200.96 * 12
≈ 2411.52 cubic cm
Comparing the volumes, we can see that the cone-shaped cup holds more popcorn since its volume is approximately 4710 cubic cm, whereas the cylinder's volume is approximately 2411.52 cubic cm. Hence, the cone-shaped cup can hold more popcorn than the cylinder.