Question

A cylinder has its height doubled and its radius cut to one third. What is the ratio of the volumes of the modified cylinder to the original cylinder?

Answer 1

do you know the formula for volume of a cylinder?

Answer 2

volume = Pi r^2 h

Answer 3

so if height is doubled and radius is cut to one third, new volume would be v = pi*(1/3)^2 * (2h) right?

Answer 4

I'm not sure but it sounds right

Answer 5

wait yeah i forgot to put something. v = pi * (r/3)^2 + 2h there that's right now. so what will be the new volume?

Answer 6

I do not know.

Answer 7

what is the square of 1/3?

Answer 8

lol wait. i have another typo sorry. v = pi*(r/3)^2 * 2h sorry bout that

Answer 9

its okay. But Idk what that is .

Answer 10

(1/3)^2 = (1)^2/(3)^2

Answer 11

so the both equal 1/9
?

Answer 12

what is the square of r?

Answer 13

i don't know

Answer 14

it's r^2

Answer 15

square of r is r squared

Answer 16

so it becomes v = pi * (1/9 r^2) * 2h what is 2 x 1/9?

Answer 17

2/9

Answer 18

so it becomes v = 2/9 * (pi * r^2 * h) do you notice something?

Answer 19

not really. lol ..sorry I'm stupid :P

Answer 20

pi*r^2*h is the original volume

Answer 21

ohhh

Answer 22

so do you know what the ratio of the modified cylinder to the original cylinder is?

Answer 23

2/9 ? right

Answer 24

close. the volume of modified clinder is 2/9* pi * r^2 * h. The volume of the original cylinder is pi * r^2 *h. so the ratio of modified to original would be \[\LARGE \frac{\frac29 \pi r^2 h}{\pi r^2 h}\]

Answer 25

what does that give you?

Answer 26

I'm not sure :S

Answer 27

pi*r^2 * h cancels out \[\LARGE \frac{\frac29 \cancel{\pi r^2 h}}{\cancel{\pi r^2 h}}\] so it becomes \[\frac{\frac29}{1}\] so the ratio is 2/9 : 1

Answer 28

Ohhhh. Okay. Thanks!!

Answer 29

if you get confused by a problem like this use actual numbers
since the answer does not depend on the actual numbers used, you will get the same answer as if you used a formula
plus it is a good check

Answer 30

and pick easy numbers. say the original cylinder has height 1 and radius 3
then the area is \(\pi \times 3^2=9\pi\)
double the height to 2, take one third of the radius get 1 now the area is
\[2\pi\] and
\[\frac{2\pi}{9\pi}=\frac{2}{9}\]