It appears that you have a derivative and want to integrate...
dy/dx=1+3√x
y(x)=x+(2/3)x^(3/2)+C you are given that f(4)=25 so we can solve for the constant of integration...
y(4)=25=4+16/3+C
21=16/3+C
(63-16)/3=C
47/3=C so
f(x)=x+(2/3)x^(3/2)+47/3
f(x)=(3x+2x^(3/2)+47)/3
I like the substitution method. Which is when you make one equation equal only x or y and plug it into the other equation)
There is also the graphing method. If you graphed it, it might not be quite as accurate (at least on hand, on computer you would be pretty exact)
Then there is the elimination method. You multiply one of the equations by a coefficient so that you can eliminate x or y from the equation.
First, we must solve for the radius of the sphere:
V=



r=(3

)

r=(3*

)

r≈5.99
Second, we must solve for surface area:
A=4


A=4*

*

A≈450.88