How do you find the volume V of the described solid S where the base of S is a circular disk with radius 4r and Parallel crosssections perpendicular to the base are squares?
1 Answer
Jul 21, 2018
Answer:
Explanation:
Place circular base on xy plane, centred at Origin.
At
#x^2 + y^2 = 16r^2#
Considering that part of the solid in the 1st octant, with the square crosssections running parallel to the xz axis, the volume of a elemental cross section is:
Thus:
Volume in 1st Octant is only
So
Reality check.

Volume of cube side
#8r# is#V_C = 512 r^3# 
Volume of sphere radius
#4r# is#V_S = (256 pi R^3)/3 = 268.083 R^3 # 
#V_S < V_("Tot") < V_C#