The total surface area of the sphere is four times the area of great circle. To know more about great circle, see properties of a sphere. Given the radius r of the sphere, the total surface area is
 

For detailed information about sphere, see the Solid Geometry entry, The Sphere.
 

The formula for the volume of the sphere is given by

Problem 694
The frame shown in Fig. P-694 is of constant cross section and is perfectly restrained at its lower end. Compute the vertical deflection caused by the couple M.
 

Problem 692
Find the value of EIδ midway between the supports for the beam shown in Fig. P-692. (Hint: Combine Case No. 11 and one half of Case No. 8.)
 

Problem 691
Determine the midspan deflection for the beam shown in Fig. P-691. (Hint: Apply Case No. 7 and integrate.)
 

Problem 690
The beam shown in Fig. P-690 has a rectangular cross section 50 mm wide. Determine the proper depth d of the beam if the midspan deflection of the beam is not to exceed 20 mm and the flexural stress is limited to 10 MPa. Use E = 10 GPa.
 

Problem 689
The beam shown in Fig. P-689 has a rectangular cross section 4 inches wide by 8 inches deep. Compute the value of P that will limit the midspan deflection to 0.5 inch. Use E = 1.5 × 10⁶ psi.