Final answer:
To find the volume of the water that would fill the glass cylinder containing two spheres, subtract twice the volume of a single sphere from the volume of the cylinder. The resulting polynomial representing the water volume is 15x³ - 26x² + 54.
Step-by-step explanation:
To calculate the volume of water that will fill the glass cylinder containing two spheres, first, we calculate the volume of both spheres and then subtract this from the volume of the cylinder. The volume of each red ball is given by the polynomial 5x³ + 11x² - 16, and there are two such balls. Hence, the combined volume of the two balls is 2(5x³ + 11x² - 16). The volume of the glass cylinder is given by the polynomial 25x³ - 4x² + 22.
To find the volume of the water, the formula used will be: Volume of cylinder - Volume of both spheres. Therefore, the volume of the water (Vw) that will fill the glass cylinder is calculated as:
Vw = Volume of cylinder - 2 × Volume of sphere
= (25x³ - 4x² + 22) - 2(5x³ + 11x² - 16)
= 25x³ - 4x² + 22 - (10x³ + 22x² - 32)
= 25x³ - 4x² + 22 - 10x³ - 22x² + 32
= (25x³ - 10x³) - (4x² + 22x²) + (22 + 32)
= 15x³ - 26x² + 54