# Thread: volume and algebra problems

1. ## volume and algebra problems

The radius of a right circular cone is doubled and its height is tripled to form a new right circular cone. What is the ratio of the volume of the original cone to the new one?
Seems to be a 1:12 ratio but I always come up with 1:6??

The variables a, b, and c are all integers and a + b + c = 50. If a < 0, and 0 < b < 30, then the minimum possible value for c is 22. Why?

2. Originally Posted by sarahh
The variables a, b, and c are all integers and a + b + c = 50. If a < 0, and 0 < b < 30, then the minimum possible value for c is 22. Why?
The maximum value for a is -1 and for b is 29. When you add them you get 28, and you need another 22 to make 50.

(I'll look up the formula for a cone just now, i forgot it again )

3. Originally Posted by sarahh
The radius of a right circular cone is doubled and its height is tripled to form a new right circular cone. What is the ratio of the volume of the original cone to the new one?
Seems to be a 1:12 ratio but I always come up with 1:6??
Right the first cone's volume is $\frac{1}{3} \pi r^2 h$

For the second cone we have: $\frac{1}{3} \pi (2r)^2 (3h)$

$\frac{1}{3} \pi r^2 h \ \ : \ \ \frac{1}{3} \pi (2r)^2 (3h)$

$r^2 h \ \ : \ \ 4r^2 (3h)$

$1 : 12$

4. Thanks for your help jandvl--those were driving me crazy!

5. Originally Posted by sarahh
Thanks for your help jandvl--those were driving me crazy!
You're welcome