Simply find the volume of each figure using their corresponding formulas and compare them! :D
CYLINDER: πr2h
CONE: πr2h ÷ 3
CYLINDER WORK:
Your radius is 2, which was a simple find! It wants it squared, so simply do 2x2 to get your squared radius of 4. Now that you know this, as well as your height, which is 3, let's plug it in!
π×4×3 (I would suggest putting this in your calculator)
=37.7
CONE WORK:
Your radius is 2 again, which was a simple find because its half your diameter, or 4! It wants it squared again, so simply do 2x2 to get your squared radius of 4. Now that you know this, as well as your height, which is 9, let's plug it in! The only difference is you have to divide your whole answer by three since it's different for a cone.
π×4× 9 ÷ 3 (I would suggest putting this in your calculator)
=37.7
Well, what a coincidence, they are the same! This proves that it does not depend on the height, it will only depend on the proportions of your shape, since the cylinder could have had a much larger scale of numbers, which would make it bigger not based on it's shape, but it's overall size.