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
The total volume of a cylinder is given by V = πr^2h. The radius of the cylinder is (5x + 2) and the height is (2x + 8).
Substitute these values into the formula:
V = π(5x + 2)^2(2x + 8)
V = π(25x^2 + 20x + 4)(2x + 8)
V = π(50x^3 + 400x^2 + 80x + 200x^2 + 1600x + 320)
V = π(50x^3 + 600x^2 + 1680x + 320)
V = 50πx^3 + 600πx^2 + 1680πx + 320π
So, the polynomial in standard form that best describes the total volume of the cylinder is 50x^3 + 600x^2 + 1680x + 320.