is what I've been doing correct so far:

find the value of h for a spherical segment whose volume is equivalent to 159pi if the radii of the bases are 5m and 4m respectively

v= (pi/6)(3a^2 + 3b^2 + h^2) h

v= 0.52 ((3)(5^2) + (3)(4^2) + h^2) h

= 0.52 ((3)(25) + (3)(16) + h^2) h

= 0.52 (75 + 48 + h^2) h

=(39 + 24.96 + 0.52h^2) h

=(63.96 + 0.52h^2) h

if yeah, how do I find the value of h?

if not, where did I go wrong?

thank youuuuu so much for any help!!

I answered you in the next thread, but I don't have time to follow your work, so I haven't checked it.

https://www.askmehelpdesk.com/math-sciences/find-value-h-327327.html

Since you know the value of v (159 pi), you can solve it using the calculator whose URL I posted.

Please help me understand the spherical segment that you are analyzing - specifically, how did you get the equation:

v= (pi/6)(3a^2 + 3b^2 + h^2) h?

Is this segment from a hemi-sphere of base radius a, with a segment cut out of height h creating an upper face of radius b? If that's the case, then the volume would be expressed as

v = pi ( a^2h - h^3)

As to solving the cubic that you got for h, you can use a numerical technique like Newton's method to determine h. Or you can look into ways of solving cubics, from here:
Cubic function - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Cubic_equation)