A cylinder has a radius of 6x + 4 and a height of 8x + 7. Which polynomial in standard
form best describes the total volume of the cylinder? Use the formula V =Пr^2 for the
volume of a cylinder.
To find the total volume of the cylinder, we need to use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius and h is the height.
Given that the radius is 6x + 4 and the height is 8x + 7, the volume of the cylinder can be calculated as follows:
V = π(6x + 4)^2(8x + 7)
V = π(36x^2 + 48x + 16)(8x + 7)
V = π(288x^3 + 384x^2 + 128x + 224x^2 + 299x + 112)
V = π(288x^3 + 608x^2 + 427x + 112)
Therefore, the polynomial in standard form that best describes the total volume of the cylinder is:
V = 288πx^3 + 608πx^2 + 427πx + 112π