Final answer:
To find the volume of a cone with a radius of 15 inches and a height of 7 inches, the formula V = (1/3)πr²h is used with k equal to 1/3, resulting in a volume of 1,575π cubic inches.
Step-by-step explanation:
The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height. Given that a cone with a radius of 6 inches and a height of 10 inches has a volume of 120π cubic inches, we can use this information to find a constant of proportionality, k, such that V = k · r² · h. To find k, we set V equal to 120π, r to 6, and h to 10, which gives k equal to 1/3 after simplifying.
Now, to find the volume of a cone with a radius of 15 inches and a height of 7 inches, we plug those values into the formula with our constant k and find that V = (1/3)π(15²)(7). After calculating, we find that V equals to 1,575π cubic inches.