A cylinder has a radius of 5x + 2 and a height of 2x + 8. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula V = r2h for the volume of a cylinder. (1 point) Responses 100x4 + 880x3 + 2256x2 + 1408x + 256 100 Image with alt text: pi x 4 + 880 Image with alt text: pi x 3 + 2256 Image with alt text: pi x 2 + 1408 Image with alt text: pi x + 256 Image with alt text: pi 50x3 + 240x2 + 168x + 32 50 Image with alt text: pi x 3 + 240 Image with alt text: pi x 2 + 168 Image with alt text: pi x + 32 Image with alt text: pi 20x3 + 168x2 + 384x + 128 20 Image with alt text: pi x 3 + 168 Image with alt text: pi x 2 + 384 Image with alt text: pi x + 128 Image with alt text: pi 10x2 + 44x + 16 10 Image with alt text: pi x 2 + 44 Image with alt text: pi x + 16 Image with alt text: pi
The volume V of a cylinder is given by V = πr^2h, where r is the radius and h is the height.
In this case, the radius is 5x + 2 and the height is 2x + 8.
Substitute the values into the formula:
V = π(5x + 2)^2(2x + 8)
V = π(25x^2 + 20x + 4)(2x + 8)
V = π(50x^3 + 40x^2 + 8x + 200x^2 + 160x + 32)
V = π(50x^3 + 240x^2 + 168x + 32)
The polynomial that best describes the total volume of the cylinder in standard form is 50x^3 + 240x^2 + 168x + 32.