Final answer:
The volume of the cone suggested by Becky is approximately 78.54 cubic inches.
Step-by-step explanation:
To calculate the volume of a cone, we can use the formula V = (1/3)πr^2h, where r is the radius and h is the height of the cone.
In this case, the slant height is 7 inches, which is equal to the hypotenuse of the right triangle formed by the slant height, height, and radius of the cone.
Using the Pythagorean theorem, we can calculate the radius as r = √(7^2 - 6^2) = √(49 - 36) = √13 inches.
Now we can plug in the values of r = √13 inches and h = 6 inches into the volume formula to get V = (1/3)π(√13)^2(6) = (1/3)π(13)(6) ≈ 78.54 cubic inches.