Final answer:
A) To find the surface area, use the formula Surface Area = 4πr². Substitute the given rate of increase in radius to calculate the surface area. B) To determine the volume, use the formula Volume = (4/3)πr³ and substitute the rate of increase in radius. C) Calculate the diameter by multiplying the radius by 2. D) The center of the sphere is located at the midpoint of the diameter, which is half the length of the diameter away from any point on the surface.
Step-by-step explanation:
A) The surface area of a sphere can be calculated using the formula: Surface Area = 4πr² where r is the radius of the sphere. As the radius is increasing at a rate of 0.3, we can substitute this value into the formula to calculate the surface area.
B) The volume of a sphere can be calculated using the formula: Volume = (4/3)πr³ where r is the radius of the sphere. With the given rate of increase in radius, we can substitute this value into the formula to calculate the volume.
C) The diameter of a sphere is equal to twice the radius. So, the diameter of a sphere with a given radius can be calculated by multiplying the radius by 2.
D) The center of a sphere is the point equidistant from all points on the surface of the sphere. It is located at the midpoint of the diameter. Therefore, we can find the center of the sphere by finding the midpoint of the diameter, which is half the length of the diameter away from any point on the surface.