To find the volume of a cylinder, you use the formula V = πr^2h, where r is the radius and h is the height of the cylinder.
Given that the radius is 2x + 3 and the height is 6x + 1, the volume can be calculated as:
V = π(2x + 3)^2(6x + 1)
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)
Thus, the polynomial in standard form that best describes the total volume of the cylinder is 24πx^3 + 78πx^2 + 72πx + 9π.
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?
3 answers
try again
Apologies for the mistake. Let's reevaluate the volume calculation:
The formula for the volume of a cylinder is: V = πr^2h
Given that the radius is 2x + 3 and the height is 6x + 1, we substitute these values into the formula:
V = π(2x + 3)^2(6x + 1)
V = π(4x^2 + 12x + 9)(6x + 1)
V = π(24x^3 + 72x^2 + 54x + 4x^2 + 12x + 9)
V = π(24x^3 + 76x^2 + 66x + 9)
Therefore, the total volume of the cylinder can be best described by the polynomial: 24πx^3 + 76πx^2 + 66πx + 9π.
The formula for the volume of a cylinder is: V = πr^2h
Given that the radius is 2x + 3 and the height is 6x + 1, we substitute these values into the formula:
V = π(2x + 3)^2(6x + 1)
V = π(4x^2 + 12x + 9)(6x + 1)
V = π(24x^3 + 72x^2 + 54x + 4x^2 + 12x + 9)
V = π(24x^3 + 76x^2 + 66x + 9)
Therefore, the total volume of the cylinder can be best described by the polynomial: 24πx^3 + 76πx^2 + 66πx + 9π.