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 = Пr^2h for the volume of a cylinder.
To find the total volume of the cylinder, we first need to substitute the given values for 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 + 190x^2 + 144x + 32)
Therefore, the polynomial in standard form that best describes the total volume of the cylinder is:
V = 50πx^3 + 190πx^2 + 144πx + 32π.