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=pie r^2h for the volume of a cylinder
The formula for the volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height.
In this case, the radius is 2x+3 and the height is 6x+1.
Substituting these values into the volume formula, we get:
V = π(2x+3)^2(6x+1)
Expanding and simplifying this expression, we get:
V = π(4x^2+12x+9)(6x+1)
V = π(24x^3+72x^2+54x+6x^2+18x+9)
V = π(24x^3+78x^2+72x+9)
Therefore, the polynomial in standard form that best describes the total volume of the cylinder is:
24πx^3 + 78πx^2 + 72πx + 9π