Help needed wtih Calculus

Question

The base of a solid in the xy-plane is the circle x² + y² = 16. Cross sections of the solid perpendicular to the y-axis are semicircles. What is the volume, in cubic units, of the solid?

Options:

1)
2)
3)
4)

Answer 1

If we consider semicircle-section with y-coordinate equel y then radius r of this section will be r = (16 - y²)^1/2.

Then area A of this section A = πr²/2 = π(16 - y²)/2. Then volume V = ∫_-4⁴ π(16 - y²)/2.dy = π∫₀⁴(16 - y²)dy = π(16y - y³/3)₀⁴ = π(64 - 64/3) = 128π/3.

Answer is 1)