Question

A cone has a volume of 6 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

A. 12 in3

B. 18 in3

C. 24 in3

D. 36 in3

Answer 1

@Mertsj

Answer 2

@SolomonZelman

Answer 3

Now let's think for a moment.
What is the formula for the volume of a cone?

Answer 4

1/3 pi(r)^2

Answer 5

Almost.

Answer 6

???

Answer 7

\[Vcylinder =πr^2h\]

Answer 8

oh "h"!!!!

Answer 9

\[V _{_{c}}=\frac{1}{3}\pi r^2h\]

Answer 10

What is the formula for the volume of a cylinder?

Answer 11

pi(r)^2(h)

Answer 12

Yes. How do the volumes compare?

Answer 13

The cone has 1/3

Answer 14

Or another way to say that is "the volume of the cylinder is 3 times the volume of the cone."

Answer 15

oh ok

Answer 16

Do you understand? Of course the radii and heights must be the same.

Answer 17

yes, but I am still confused how to figure out the volume of the cylinder so the cone can fit in it.

Answer 18

The question only gives me the volume of the cone, do I just multiply that number by 3?

So 6 * 3 = 18?

Answer 19

Are you there?
@Mertsj

Answer 20

yes and yes

Answer 21

ok so 18 is the answer?

Answer 22

Can I ask you another question?

Answer 23

yes. The idea is that if you have a cylinder and cone of equal radii and height, then 3 of the cones will fit in the cylinder.

Answer 24

ok

Answer 25

Hold on one sec, I have one more question

Answer 26

Are you going to post it or am I supposed to guess what it is?

Answer 27

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.) (1 point)


4.71 minutes
3.14 minutes
14.13 minutes
9.42 minutes

Answer 28

How do you upload an image?

Answer 29

We're talking about a cone here so just calculate the volume of the cone in cubic inches.

Answer 30

Divide that answer by 14 and that will be the number of minutes.

Answer 31

The image is a conical funnel

Answer 32

Find the volume of the cone.

Answer 33

the volume of the cone is 9.42, right?

Answer 34

What is the radius of the cone?

Answer 35

3 in

Answer 36

What is the height of the cone?

Answer 37

oh wait I forgot to multiply the height!

Answer 38

the height is 7 in

Answer 39

65.94 is the volume

Answer 40

I think the answer is 4.71 correct?

Answer 41

\[V=\frac{1}{3}(3.14)(3^2)(7)=65.94\in^3\]

Answer 42

ok that's what I got

Answer 43

\[\frac{65.94}{14}=4.71minutes\]

Answer 44

ok thanks!

Answer 45

Do you mind helping me with some more? I don't what to keep you though.