Final answer:
The volume of a solid sphere is V = 4/3 π r³ and the surface area is A = 4 π r². For a sphere with both an inner radius (r1) and an outer radius (r2), the formulas adjust to V = 4/3 π (r2³ - r1³) for volume and A = 4 π r2² + 4 π r1² for surface area.
Step-by-step explanation:
Formulas for a Solid Sphere with Inner and Outer Radii
The formulas for the surface area and volume of a solid sphere are based on the radius of the sphere. However, when a sphere has both an inner and outer radius, it is known as a spherical shell, and we must calculate the values for both radii separately. The volume of a solid sphere is given by the formula V = 4/3 π r³, where V is the volume and r is the radius of the sphere. For a spherical shell with an inner radius r1 and an outer radius r2, the volume is the difference between the volume of the outer sphere and the inner sphere, calculated as V = 4/3 π (r2³ - r1³). The surface area of a solid sphere is given by the formula A = 4 π r², where A is the surface area and r is the radius of the sphere. For a spherical shell, the total surface area is the sum of the outer and inner surface areas, which is A = 4 π r2² + 4 π r1². Remember that in these equations, π (pi) is a mathematical constant approximately equal to 3.14159. The raised number (e.g., r³) indicates that the radius is being cubed or squared.