Determine the radius of a cylinder

[nikita.s]

A cylinder has a colume of 200pi cm^3. Its height is 3 cm greater than its radius. Determine the radius of the cylinder.

I kept getting this one wrong and I don't know how to do it correctly.

Since the height is 3x greater than the radius, I did:

3h = r

Then I plugged in the variable into the volume of a cylinder equation.

V = pi r^2 h
200pi = pi (3h)^2 h
200 = 9h^3
2.8 = h

Then I plugged the h back into 3h = r, and I got 8.43 = r.

The answer is supposed to be 5. How do I get to that?

 

[tkhunny]

Try:

r = r
h = r+3

Edit: Corrected.

 

[skeeter]

Try:

r = r
h = 3r

???

A cylinder has a colume of 200pi cm^3. Its height is 3 cm greater than its radius. Determine the radius of the cylinder.

$\displaystyle h = r + 3$

$\displaystyle V = \pi r^2 h$

$\displaystyle V = \pi r^2 (r + 3)$

$\displaystyle 200 \pi = \pi r^2 (r + 3)$

$\displaystyle 200 = r^3 + 3r^2$

$\displaystyle r^3 + 3r^2 - 200 = 0$

$\displaystyle r = 5 cm$

 

[nikita.s]

Ah! What a stupid mistake.. lol
Thank you!