Problema Solution
The radii of the bases of a spherical segment are 6 inches and 11 inches, and the perpendicular distance between the bases is 5 inches. Find the volume and total area of the segment?
Answer provided by our tutors
We assume the radius is R, so we have the following equation:
sqrt(R^2 - 11^2) + 5 = sqrt(R^2 - 6^2)
We solve it
R = 12.53 inches
So
the total area of the segment V= V2 - V1
V2 = 1/3 * pi*(3*12.53 - 6.53)*6.53^2 = 1386.2 cubic inches
V1 = 1/3 * pi*(3*12.53 - 1.53)*1.53^2 = 88.4 cubic inches
So Volume of segment = V2 - V1 = 1386.2 - 88.4 = 1297.9 cubic inches