What would be the induced EMF of a hollow sphere moving in linear direction transverse to a constant magnetic field?

This is how I visualized the question-

Now, as we know, induced EMF is the change in magnetic flux-

$$
EMF = − frac{NDeltaPhi}{Delta t}
$$

And as for the magnetic flux-

$$
Phi_B = iint_A textbf{B} cdot dtextbf{A}
$$

I know that it requires a changing area in a given time.

My visual intuition on it was like this-

The geometrical structure that emerge from the change of are in a given time is a capsule.

It’s formula for the are is:

$$
S = 2pi r(2r + l)
$$

I previously derived induced EMF formula for a rod and metal sheet. It didn’t require much calculus. My instinct says in this question we have to use calculus.

Because the area of the sphere is curved and magnetic flux differs on every point, right?

I wish I could approach these ideas mathematically, I maybe missing many ideas though.

Would you please take a look?