cone has height twice its radius, volume of 18pi in^3; find cone's height in inches

[tathagata7]

I'm studying for my SSAT and have this word problem:

A cone has a height twice its radius and a volume of [FONT=MathJax_Main]18[FONT=MathJax_Math-italic]π[/FONT][FONT=MathJax_Main] [/FONT][FONT=MathJax_Math-italic]i[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]3[/FONT]18π in3.[/FONT]
What is the cone’s height, in inches?
(Volume of a cone [FONT=MathJax_Main]=[FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]π[/FONT][FONT=MathJax_Math-italic]r[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math-italic]h)[/FONT]


I'm trying to derive the answer 6

While I'm studying geometry, I cannot figure this out.

Thank you so much,

Carrie[/FONT]

 

[stapel]

A cone has a height twice its radius and a volume of [FONT=MathJax_Main][FONT=MathJax_Math-italic][/FONT][FONT=MathJax_Math-italic][/FONT][FONT=MathJax_Math-italic][/FONT][FONT=MathJax_Main][/FONT]18π in³.[/FONT]
What is the cone’s height, in inches?
(Volume of a cone [FONT=MathJax_Main]=[FONT=MathJax_Main] (1/[/FONT][FONT=MathJax_Main]3)[/FONT][FONT=MathJax_Math-italic]π[/FONT][FONT=MathJax_Math-italic]r[/FONT]^{[FONT=MathJax_Main]2[/FONT]}[FONT=MathJax_Math-italic]h)[/FONT]

I'm trying to derive the answer 6

While I'm studying geometry, I cannot figure this out.[/FONT]

A good start might be to use the information they've given you. They've told you that h = 2r and that V = 18pi. They've given you the relationship between the volume V, the height h, and the radius r. So plug the value and expressions they've given you into the formula they've given you, and see where that leads.

 

[HallsofIvy]

I'm studying for my SSAT and have this word problem:

A cone has a height twice its radius and a volume of [FONT=MathJax_Main]18[FONT=MathJax_Math-italic]π[/FONT][FONT=MathJax_Main] [/FONT][FONT=MathJax_Math-italic]i[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]3[/FONT]18π in3.[/FONT]
What is the cone’s height, in inches?
(Volume of a cone [FONT=MathJax_Main]=[FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math-italic]π[/FONT][FONT=MathJax_Math-italic]r[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math-italic]h)[/FONT]

No, it isn't. The volume of a cone with radius r and height h is \(\displaystyle V= \frac{1}{3}\pi r^2 h\).
I presume that is what you intended to write but it did not come out that way!

I'm trying to derive the answer 6

While I'm studying geometry, I cannot figure this out.

Thank you so much,

Carrie[/FONT]

You are told that the volume is \(\displaystyle 18\pi\) cubic inches so replace V with that. You are told that the height is twice the radius so replace h with 2r:
\(\displaystyle 18\pi= \frac{1}{3}\pi r^2(2r)= \frac{2}{3}\pi r^3\)
Divide both sides by \(\displaystyle (2/3)\pi\): \(\displaystyle \left(\frac{3}{2\pi}\right)18\pi= 27= r^3\).

Can you solve that?

 

[tathagata7]

Thank you!

Thank you everyone for your reply :-D.

I understand now.

I was over reading the problem.

Once I got to:

18pi = 1/3pi r² height
18pi = 1/3pi r² 2r
18pi = 2/3pi r³

I understand how to proceed to 3 which times twice equals the answer 6.