Given a soda can with a volume of 21 and a diameter of 6, what is the volume of a cone that fits perfectly inside the soda can?

Question

calculusxy · Answer

The volume of a cone that fits into a cylinder would be exactly 1/3 of the volume of the cylinder. 

In other words, it would take three cones to fill the space inside of the cylinder that it fits in.

calculusxy · Answer

The fact that the soda can (cylinder) has a diameter of 6 should not interfere much with the approach to solving this problem. As long as we know the volume of the soda can (which is 21), it should be sufficient to solve the problem.

calculusxy · Answer

Knowing that the volume of the cone would be 1/3 of the volume of the cylinder, what do you think would be the volume of the cone for this problem?

jilltalks · Answer

I don't know how to find the volume of the cone.

calculusxy · Answer

The volume of the cylinder (soda can) is 21. 

The volume of the cone would be one-third of 21. What would that be?

jilltalks · Answer

What would the formula be?

jilltalks · Answer

7?

calculusxy · Answer

The general formula would be: 
$$\frac{\pi r^2 h}{3} = \text{Volume of Cone}$$

calculusxy · Answer

Yes! @Jilltalks

calculusxy · Answer

I am pretty sure that if you were to use the formula to find the volume of the cone, then you would have to, perhaps, approximate it to 7.

jilltalks · Answer

would 7 be the answer?

calculusxy · Answer

Yes, that's what I think.

jilltalks · Answer

thank you so much!

calculusxy · Answer

No problem :)