Question

Given a soda can with a volume of 36 and a diameter of 4, what is the volume of a cone that fits perfectly inside the soda can?

Answer 1

volume of the can = pi r^2h = 36
r = 1/2 * 4 = 2
so
36 = pi*2^2 * h
h = 36 / 4 pi

Answer 2

given that volume of the cone thet fits into the can = (1/3) pi r^2 h
can you find this volume?
h = 36/4pi = 9/pi and r = 2

Answer 3

2.9

Answer 4

oh - there was no need for me to do all this!!

Answer 5

9/pi is 2.9 when rounded to the nearest tenth

Answer 6

and thank you so much!

Answer 7

as the volume of the cone = 1/3 * volume of the cylinder
the answer is 1/3 * 36 = 12

Answer 8

so the final answer would be 12?

Answer 9

yes - there was no need to do all those calculations!! - the volume of the cone is 1/3 times the volume of the cylinder

Answer 10

V can = pi r^2 h
V cone = (1/3 pi r^2 h

r and h is the same for both can and cone

Answer 11

I don't know why I didn't see that in the first place!!

Answer 12

do you follow what wrote?

Answer 13

its not 2.9
9/pi is the height of the the can ( and the cone)

Answer 14

okay, the final answer is 12

Answer 15

I think. Haha

Answer 16

if we substitute h = 9/pi into the formula for the volume of the cone we get 12 which confirms the result

Answer 17

Okay. Thank you so much! (: