I have the height and volume of a tank but I cannot find the radius. Can someone help?

Question

Equation- PI(r^2)(h)+4/3(PI(r^3)=22
How do I find the radius?

Answer 1

This is a strangely shaped tank - apparently it's a cylinder with a sphere of the same radius sitting on top of it, or something equivalent.

Anyway, the easiest way to find solutions for this will be numerically. There will only be one solution for positive r (since the derivative of the LHS with respect to r is 4πr^2 + 2πrh which is positive for all positive r). So take an initial guess and refine it with Newton-Raphson or something similar. Since you haven't given the value of h, I can't give you a specific answer.

Answer 2

for one don't use PI when actually talking about Pi.
PI stands for personal investigator, personal ...
Pi stands for the mathematical number that can find the circumfrence, diameter, volume of a cylinder, etc.
Pi is represented by the greek symbol of p of which is π. yes there are two more greek p's out there but only π is mathematical to your problem. by the way Pi = π ≈ 3.141592653589793238462643383279502884197169399375105820.... but in math it's just 3.14.

so to solve ur prob. a=πr²
V-cylinder= b*h
b= πr²

so

V-cylinder=πr²h.

but from ur formula u gave, the tank must be a sphere.
to find the radius of a shpere, you have...
SA*(½+¼)/h/π²
and that should get u ur r^3
and find the cube root from there

Answer 3

Im not a math whiz but cant you only find the radius of a circle since the radius is half the diameter?

Answer 4

The radius is half of your answer so your answer would be 11.