Question

Make h the subject of the formula A=πr²tπr√h²+r²

Answer 1

Did you mean A=πr²tπr√(h²+r²) , really different from what you wrote!!
A = π^2 r^3 t √(h²+r²)
√(h²+r²) = A/(π^2 r^3 t)
square both sides
h^2 + r^2 = A^2/(π^4 r^6 t^2)
h^2 = A^2/(π^4 r^6 t^2) - r^2
h = √( A^2/(π^4 r^6 t^2) - r^2 )

somehow I don't think this is what you meant

Answer 2

It looks like the area of a cone
A = πr² + πr√h²+r²
A - πr² = πr√(h²+r²)
(A - πr²)/(πr²) = √(h²+r²)
h²+r² = ((A - πr²)/(πr²))²
h² = ((A - πr²)/(πr²))² - r²
h = √(((A - πr²)/(πr²))² - r²)

Answer 3

@Reiny I think that "t" might be a + sign.