1. The problem statement, all variables and given/known data As quoted from the question sheet: When building a tall support, often the self weight of the support must be considered. For an optimal support, the volume of material, and hence the cost, will be a minimum. If the maximum allowable stress in concrete is 12 MPa, determine the optimal geometry of a column 100 metres tall made of concrete to support a mass of 1000 tonnes at its top. (Hint: think of the shape of the CN tower) (from a table of values) The weight per cubic meter of concrete is 24 kN/m^3, or 24000 N/m^3. Use 9.81 m/s^2 as the value of gravitational acceleration. 2. Relevant equations Stress = Force per area = F/A A of a circle = pi(d^2)/4, where d is the diameter Volume of a cylinder = Ah, A = pi(d^2)/4 3. The attempt at a solution 1000 tonnes = 1.0 E6 kg, so the weight of the mass = 1E6 kg x g = 9.81E6 N Maximum stress of concrete is 12 MPa = 12E6 Pa 12E6 Pa = (9.81E6 N + (100m)pi(r^2)(24000 N/m^3))/(pi*r^2) Radius of column = 0.57 m Is that the correct approach? Thanks in advance.