a cylinder has a radius of 2x+3 and a height of 6x+1. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula V=pi r^2h
To calculate the volume of the cylinder, we substitute the given formula V=pi r^2h with our values for the radius and height:
V = pi(2x + 3)^2(6x + 1)
V = pi(4x^2 + 12x + 9)(6x + 1)
V = pi(24x^3 + 72x^2 + 54x + 6x^2 + 18x + 9)
V = pi(24x^3 + 78x^2 + 72x + 9)
Therefore, the polynomial in standard form that best describes the total volume of the cylinder is:
V = 24πx^3 + 78πx^2 + 72πx + 9π.