Betty closes the nozzle of the funnel and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 14 cubic inches per minute, how long will it take for all the liquid in the funnel to pass through the nozzle? (Use π=3.14.)

4.71 minutes

3.14 minutes

14.13 minutes

9.42 minutes

Question

Betty closes the nozzle of the funnel and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 14 cubic inches per minute, how long will it take for all the liquid in the funnel to pass through the nozzle?  (Use π=3.14.)

 4.71 minutes

 3.14 minutes

 14.13 minutes 
    

 9.42 minutes

anonymous · Answer

attachment

anonymous · Answer

@Directrix

anonymous · Answer

@Directrix

directrix · Answer

I'm thinking.

directrix · Answer

Do you know the volume of the funnel? I think its shape is that of a right circular cone.

anonymous · Answer

I guess you are right, it doesn't say specifically @Directrix

directrix · Answer

Let's try something.

Volume of right circular cone is given by the formula:

V = (1/3) * pi * r^2 * h where r is the radius of the circular base and h is the height of the cone.

anonymous · Answer

i got 65.94

directrix · Answer

@tlovesmath   Wow, I was just getting ready to ask you to calculate that.

If 65.94 cubic units is the volume of the cone (I got 65.973  using more digits of pi), then ....

directrix · Answer

... divide 65.973 cubic units by 14 cubic units per minute to see how many minutes it takes for the funnel to empty.

directrix · Answer

Lemme know what you get.

anonymous · Answer

4.7 @Directrix

anonymous · Answer

Can I ask you one more question?

directrix · Answer

I'm wondering if there is water in the snout of the funnel that should be considered in this problem. I suppose not.

anonymous · Answer

A company makes similar cylindrical containers in two sizes, as shown in the table below. 
  


What is the volume, in cubic centimeters, of Type 2 containers?
 4826.12

 6434.8

 2041.12

 3619.6

anonymous · Answer

@Directrix

directrix · Answer

Here's the theorem we need:

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

anonymous · Answer

I already got the answer but thank you :)

directrix · Answer

The two cylinders are given to be similar.

So, (9/12)^3 = 2714.69/x   where x is the volume of the Type 2 cylinder.

Solve for x. Let's see what we get.

@tlovesmath

directrix · Answer

@tlovesmath   What's going on with the calculation?

anonymous · Answer

The Answer To This Question is 6434.8 :D