Solid Geometry

Problem
A meteorologist is inflating a spherical balloon with a helium gas. If the radius of a balloon is changing at a rate of 1.5 cm/sec., express the volume V of the balloon as a function of time t (in seconds). Hint: Use composite function relationship V_sphere = 4/3 πr³ as a function of x (radius), and x (radius) as a function of t (time).

Problem
A conical tank in upright position (vertex uppermost) stored water of depth 2/3 that of the depth of the tank. Calculate the ratio of the volume of water to that of the tank.

Problem
A 523.6 cm³ solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.