How do you solve a closed cylinder with a flat bottom and an inverted?
How do you solve a closed cylinder with a flat bottom and an inverted hemispherical top where it has a height of H cm and a base radius of r cm, and we are given a design constraint such that H + 2r = 110 cm. height in terms of r? Does solve mean find the volume? As I read the question, it seems to be asking for the volume (in terms of its radius) of an upright cylinder with half a sphere removed from the top. Might it be solved by finding the volume of the cylinder, then subtracting half a sphere of the same radius? The volume of the cylinder is: pi (r)^2 h where pi will remain pi, not its numerical equivalent. r is the radius of the base as well as the sphere h is the height, which has been specified as 110 - 2r V (of cyl) = pi (r)^2 (110 -2r) V (of hemi-sphere) = 1/2 of 4/3 pi (r)^3 = 2/3 pi (r)^3 V (cyl minus hemi-sphere) = [pi (r)^2 (110 -2r)] - [2/3 pi (r)^3] V (c-h) = [110 pi (r)^2 - 2 pi (r)^3] - [2/3 pi (r)^3] V (c-h) = 110 pi (r)^2 - (8 pi (r)^3)/3) V (cyl-hemi) = (pi (r)^2) ( 110 - 8r/3) That is the volume in terms of r.