The rate of change of volume of a sphere with a radius expanding at 50 cm/min is approximately 4π cm^3/min.
The rate of change of volume of a sphere is directly proportional to the rate of expansion of its radius. This means that as the radius expands at a faster rate, the rate of change of volume also increases.
No, the rate of change of volume of a sphere cannot be negative. As the radius expands, the volume of the sphere will always increase, resulting in a positive rate of change of volume.
The rate of change of volume of a sphere can be calculated using the formula dV/dt = 4πr^2dr/dt, where dV/dt represents the rate of change of volume, r represents the radius, and dr/dt represents the rate of change of the radius.
Yes, the rate of change of volume of a sphere is directly proportional to the size of the sphere. As the sphere gets larger, the rate of change of its volume will also increase.