Answer:
Cone-shaped ≈ 716 cm^3
Cylindrical-shaped ≈ 754 cm^3
Step-by-step explanation:
Given:
Jason decides to see a movie. When he arrives at the snack counter to buy his popcorn, he has two choices in the shape of the popcorn container.
Cone Shaped Pop Corn container
- Diameter - 12 cm
- Height - 19 cm
Cylindrical Pop Corn container
- Diameter - 8 cm
- Height - 15 cm
Find the volume of the CONE container. SHOW YOUR WORK (type the formula, substitute radius and heigh, then give the final answer). l
Cone Shaped Pop Corn container
To find the volume of a cone-shaped popcorn container, we can use the formula for the volume of a cone, which is:
[tex]V = \frac{1}{3} \pi r^2 h[/tex]
where:
- V is the volume,
- r is the radius of the base,
- h is the height of the cone,
- [tex]\pi[/tex] is a mathematical constant, approximately equal to 3.14159.
Given that the diameter of the cone-shaped container is 12 cm, we can find the radius [tex]r[/tex] by dividing the diameter by 2:
[tex] r = \frac{12 \, \text{cm}}{2} = 6 \, \text{cm}[/tex]
The height ([tex] h [/tex]) of the cone is given as 19 cm.
Substituting these values into the formula gives us:
[tex]V = \frac{1}{3} \pi (6 \, \text{cm})^2 \cdot 19 \, \text{cm} = \frac{1}{3} \pi \cdot 36 \, \text{cm}^2 \cdot 19 \, \text{cm}[/tex]
[tex]V = \frac{1}{3} \cdot 3.14159 \cdot 684 \, \text{cm}^3[/tex]
[tex]V = 3.14159 \cdot 228 \, \text{cm}^3[/tex]
[tex]V = 716.1974 \, \text{cm}^3[/tex]
Therefore, the volume of the cone-shaped popcorn container is approximately [tex]716.1974 \, \text{cm}^3[/tex] or rounded to [tex]716 \, \text{cm}^3[/tex].
Cylindrical Pop Corn container
To find the volume of a cylindrical popcorn container, we use the formula for the volume of a cylinder, which is:
[tex]V = \pi r^2 h [/tex]
where:
- V is the volume,
- r is the radius of the base,
- h is the height of the cylinder,
- [tex]\pi[/tex] is approximately 3.14159.
Given that the diameter of the cylindrical container is 8 cm, the radius ( r ) can be found by dividing the diameter by 2:
[tex]r = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm}[/tex]
The height ( h ) of the cylinder is given as 15 cm.
Substituting these values into the formula gives us:
[tex]V = \pi (4 \, \text{cm})^2 \cdot 15 \, \text{cm} = \pi \cdot 16 \, \text{cm}^2 \cdot 15 \, \text{cm}[/tex]
[tex]V = 3.14159 \cdot 240 \, \text{cm}^3[/tex]
[tex]V = 753.9824 \, \text{cm}^3[/tex]
Therefore, the volume of the cylindrical popcorn container is approximately [tex] \sf 753.9824 \, \text{cm}^3[/tex] or rounded to [tex]754 \, \text{cm}^3[/tex].
