Respuesta :
Answer:
Sharing cone holds 9 times more popcorn than a skinny cone.
Step-by-step explanation:
Height of each cone = 9 inches
Radius of the sharing size cone = 3 times radius of the skinny size cone
Let the radius of skinny size cone = r
Then radius of the sharing size cone = 3r
Volume of the sharing size cone = [tex]\frac{1}{3}(\pi )(\text{Radius})^{2}(\text{Height})[/tex]
                           = [tex]\frac{1}{3}(\pi )(3r)^{2}(9)[/tex]
                           = 27πr²
Volume of the skinny size cone = [tex]\frac{1}{3}(\pi )(\text{Radius})^{2}(\text{Height})[/tex]
                            = [tex]\frac{1}{3}(\pi )(r)^{2}(9)[/tex]
                            = 3πr²
Ratio of the volumes = [tex]\frac{\text{Volume of sharing size cone}}{\text{Volume of skinny size cone}}[/tex]
                  = [tex]\frac{27\pi r^{2}}{3\pi r^{2} }[/tex]
                  = 9
Therefore, sharing cone holds 9 times more popcorn than a skinny cone.
