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.
To find the total volume of the cylinder, we need to substitute the given values of the radius and height into the formula for the volume of a cylinder:
V = π * (5x + 2)^2 * (2x + 8)
V = π * (25x^2 + 20x + 4) * (2x + 8)
V = π * (50x^3 + 160x^2 + 40x + 8x^2 + 32x + 8)
V = π * (50x^3 + 168x^2 + 72x + 8)
V = 50πx^3 + 168πx^2 + 72πx + 8π
Therefore, the polynomial in standard form that best describes the total volume of the cylinder is:
50πx^3 + 168πx^2 + 72πx + 8π