11. a cylinder has a radius of 4x + 2 and a height of 5x + 4. which polynomial in standard form best describes the total volume of the cylinder? use the formula v = pir2h for the volume of a cylinder. (1 point) 80pix3 + 144pix2 + 84pix + 16pi 20pix2 + 26pix + 8pi 80pix3 + 144pix2 + 84pix – 16pi 400pix4 + 1040pix3 + 996pix2 + 416pix + 64pi

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