Expressing h in terms of x Cone/Sphere non-calc

1. Apr 1, 2007

thomas49th

How do I do:

the formula for volume of a cone is $$\frac{1}{3} \pi r^{2}h$$
and for sphere volume is $$\frac{4}{3} \pi r^{3}$$

It says express h in terms of x, so the equation will look somthing like

x =

Can someone give me help on how to rearrange this formula?
Thx

2. Apr 1, 2007

f(x)

equate the volumes and replace r with appropriate values

3. Apr 1, 2007

cristo

Staff Emeritus
You don't have an equation to rearrange yet! You need to express the volumes of the cone and sphere in terms of the variables you are given in this question. Note that "r" for the cone is not equal to "r" for the sphere in this case. What is each one equal to?

Once you have found this, you know that the volumes of the two objects are equal. This should enable you to obtain an equation.

4. Apr 1, 2007

thomas49th

$$v = \frac{1}{3} \pi x^{2}h$$

$$v = \frac{4}{3} \pi (2x)^{3}$$

5. Apr 1, 2007

cristo

Staff Emeritus
Ok, now the volumes are the same, so can you combine these into one equation?

6. Apr 1, 2007

sutupidmath

what u need to do now is to equal the two right sides, like doing v=v, just substitute the both expressions for v. then try to multiply by 3 and then divide by (pi*x^2) and you will get h in terms of x.

7. Apr 1, 2007

sutupidmath

and the equation will look something like

h=

8. Apr 1, 2007

thomas49th

$$\frac{4}{3} \pi x^{3}$$ = $$\frac{1}{3} \pi x^{2}h$$

$$\frac{4}{3} \pi 8x^{3}$$ = $$\frac{1}{3} \pi x^{2}h$$

divide by $$\frac{1}{3} \pi x^{2}$$

gives

$$h = 32x$$

is that right?

9. Apr 1, 2007

Chele

I did the math and that's what I got too.

10. Apr 2, 2007

sutupidmath

yeah i guess that's right. good job

11. Apr 4, 2007

thomas49th

how come I cant edit these posts anymore... the edit button is gone. I can do it with other threads. I want to edit post 8, change $$\frac{4}{3} \pi x^{3}$$
to $$\frac{4}{3} \pi 2x^{3}$$

EDIT: I can edit post, but not my previous

12. Apr 4, 2007

cristo

Staff Emeritus
You can only edit upto 24 hours after posting.