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.%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A100x4 + 880x3 + 2256x2 + 1408x + 256%0D%0A100 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%0D%0A%0D%0A50x3 + 240x2 + 168x + 32%0D%0A50 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%0D%0A%0D%0A20x3 + 168x2 + 384x + 128%0D%0A20 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%0D%0A%0D%0A10x2 + 44x + 16
The formula for the volume of a cylinder is V = r^2h.
In this case, the radius is 5x + 2 and the height is 2x + 8.
Substituting the values into the formula, we get V = (5x + 2)^2(2x + 8).
Expanding this expression gives V = (25x^2 + 20x + 4)(2x + 8).
Multiplying the binomials gives V = 50x^3 + 200x^2 + 100x + 200x^2 + 800x + 320.
Simplifying further gives V = 50x^3 + 400x^2 + 900x + 320.
Therefore, the polynomial in standard form that best describes the total volume of the cylinder is 50x^3 + 400x^2 + 900x + 320.