Question

Please help me??
How many times larger is the new volume of a cylinder if only the height doubled, and the radius remained the same?

Answer 1

i think it is 2x bigger?

Answer 2

@dan815

Answer 3

You have a 3-dimensional object, and you only changed one dimension, right? That means the new volume is simply the old volume * the scale factor.

Answer 4

If the height stayed the same, but the radius doubled, what would happen to the volume?

Answer 5

gets bigger

Answer 6

well, yes. how much :-)

Answer 7

2x

Answer 8

so i am right?

Answer 9

mmm, no. Think of it this way: the volume of the cylinder is the height time the area of the base, right? The area of the base is proportional to the radius squared, right?

Answer 10

So if you double the height, the new V is the area of the base * 2*times the old height, so new V = area of base * old height * 2 which is old volume * 2

Answer 11

4?

Answer 12

bingo!

Answer 13

thanks!

Answer 14

you have to apply the scale factor to as many dimensions as changed. If you have a line, and you double the length, the length is doubled, duh. If you have a square and double one dimension, the area doubles. If you doubled both dimensions, then it is 2*2 = 4. If you doubled one dimension and tripled the other it would be 2*3 = 6. in 3 D, you have 3 dimensions to keep track of, like the cylinder base is a 2 d thing (circle) so when the radius doubles, it is 2*2 in addition to whatever happened to the height.