Thread: 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?

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 )

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

For the second cone we have:

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

Originally Posted by sarahh

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

You're welcome