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? Use the formula V = pir2h for the volume of a cylinder.
Responses
100pix4 + 880pix3 + 2256pix2 + 1408pix + 256pi
50pix3 + 240pix2 + 168pix + 32pi
20pix3 + 168pix2 + 384pix + 128pi
10pix2 + 44pix + 16pi
The correct response is 20pi x^3 + 168pi x^2 + 384pi x + 256pi.
To get this answer, first substitute the radius (5x + 2) and height (2x + 8) into the formula V = pi * r^2 * h. This gives you V = pi * (5x + 2)^2 * (2x + 8).
Next, expand and simplify the expression to get V = pi * (25x^2 + 20x + 4) * (2x + 8).
This further simplifies to V = pi * (50x^3 + 240x^2 + 168x + 32).
Therefore, the final polynomial in standard form that describes the total volume of the cylinder is 20pi x^3 + 168pi x^2 + 384pi x + 256pi.