## anonymous one year ago 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

1. anonymous

@Mertsj

2. anonymous

@SolomonZelman

3. Mertsj

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

4. anonymous

1/3 pi(r)^2

5. Mertsj

Almost.

6. anonymous

???

7. anonymous

$Vcylinder =πr^2h$

8. anonymous

oh "h"!!!!

9. Mertsj

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

10. Mertsj

What is the formula for the volume of a cylinder?

11. anonymous

pi(r)^2(h)

12. Mertsj

Yes. How do the volumes compare?

13. anonymous

The cone has 1/3

14. Mertsj

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

15. anonymous

oh ok

16. Mertsj

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

17. anonymous

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

18. anonymous

The question only gives me the volume of the cone, do I just multiply that number by 3? So 6 * 3 = 18?

19. anonymous

Are you there? @Mertsj

20. Mertsj

yes and yes

21. anonymous

ok so 18 is the answer?

22. anonymous

Can I ask you another question?

23. Mertsj

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.

24. anonymous

ok

25. anonymous

Hold on one sec, I have one more question

26. Mertsj

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

27. anonymous

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

28. anonymous

How do you upload an image?

29. Mertsj

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

30. Mertsj

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

31. anonymous

The image is a conical funnel

32. Mertsj

Find the volume of the cone.

33. anonymous

the volume of the cone is 9.42, right?

34. Mertsj

What is the radius of the cone?

35. anonymous

3 in

36. Mertsj

What is the height of the cone?

37. anonymous

oh wait I forgot to multiply the height!

38. anonymous

the height is 7 in

39. anonymous

65.94 is the volume

40. anonymous

I think the answer is 4.71 correct?

41. Mertsj

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

42. anonymous

ok that's what I got

43. Mertsj

$\frac{65.94}{14}=4.71minutes$

44. anonymous

ok thanks!

45. anonymous

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

Find more explanations on OpenStudy