Final Answer:
The combined volume of the two spherical storage tanks can be represented by the function V(r) = (4/3)π(r³ + (2r)³), where 'r' is the radius of the smaller tank.
Step-by-step explanation:
The combined volume of two spherical tanks is the sum of their individual volumes, given by the formula V = (4/3)πr³, where 'r' is the radius. In this scenario, let 'r' represent the radius of the smaller tank, and since the radius of the larger tank is twice the radius of the smaller tank, the radius of the larger tank is 2r.
The combined volume function V(r) is expressed as the sum of the volumes of the two spheres:
Simplifying this expression results in the final representation of the combined volume function V(r) = (4/3)π(r³ + (2r)³). This function provides a mathematical model for the combined volume in terms of the radius of the smaller tank.
Understanding and applying such mathematical models are crucial for solving real-world problems involving geometric shapes. In this case, the function allows for the calculation of the combined volume of the two spherical storage tanks based on the given relationship between the radii of the tanks.