The volume of a right circular cone varies jointly as the altitude and the square of the radius of the base. If the volume of the cone is 154 cu. in. when its altitude is 12 in. and the radius of the base is 3 1/2 in., find the altitude when the volume of the cone is 77 cu. in. and the radius of the base is 2 1/3 in

Question

tkhunny · Answer

"The volume of a right circular cone varies jointly as the altitude and the square of the radius of the base."

This means $Volume = k\cdot Altitude\cdot Radius^{2}$

Use the given information, substituted into the equation, to solve the problem.

anonymous · Answer

I need to know many inches the altitude is

mathstudent55 · Answer

Using the formula that tkhunny gave you, plug in the known set of data, V = 154, Altitude = 12, and r = 3.5 and get a value for k.
Then rewrite the formula with that known value of k, plug in the second volume and radius, and solve for altitude.

anonymous · Answer

When I worked it out like that I got 9 as the final altitude, which turned out to be wrong...

tkhunny · Answer

Let's see you rwork!  We'll keep a sharp eye for where you wandered off.

anonymous · Answer

$$\frac{15 }{ 12(7/2)^2 } = \frac{ 77 }{ x(7/3)^2 }$$
The answer is : 13.5
use the joint variation equation