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?
please I'm failing math. please give answers!
To find the volume of a cylinder, we use the formula V = πr^2h, where V is the volume, π is a constant (approximately 3.14159), r is the radius, and h is the height.
In this case, the radius of the cylinder is given as 5x+2 and the height is given as 2x+8. To find the total volume, we need to substitute these values into the formula.
First, we square the radius. (5x+2)^2 = 25x^2 + 20x + 4.
Then, we multiply the squared radius by the height. (25x^2 + 20x + 4)(2x+8) = 50x^3 + 180x^2 + 160x^2 + 640x + 8x + 32.
Finally, we combine like terms and write the polynomial in standard form.
The total volume polynomial in standard form for the given cylinder is: 50x^3 + 340x^2 + 648x + 32.
steve, that actually helped a lot, thank you so much!
since you give no choices, I'll just say that
v = pi r^2 h
v = pi (5x+2)^2 (2x+8)
expand that as necessary to conform to the format of the choices