The first choice, 80πx³+144πx²+84πx+16π is correct.
The formula for the volume of a cylinder is V = πr²h. Using the expressions we have for radius and volume, we have:
V = π(4x+2)²(5x+4)
= π(4x+2)(4x+2)(5x+4)
Multiplying the first two binomials, we have:
π(4x*4x+4x*2+2*4x+2*2)(5x+4)
= π(16x²+8x+8x+4)(5x+4)
= π(16x²+16x+4)(5x+4)
Multiplying by the last binomial, we have:
π(16x²*5x+16x*5x+4*5x+16x²*4+16x*4+4*4)
= π(80x³+80x²+20x+64x²+64x+16)
= π(80x³+144x²+84x+16)
= 80πx³+144πx²+84πx+16π
