A silo is to be constructed in a form of a cylinder ( only one of two bases included) topped by a hemisphere. The construction cost per square unit of surfce area for the hemisphere is 2.0 times as much as for the cylinder and the volume must be 590000 ft^3. If the construction cost are to be minimized, what should the radius be?? ** round to the nearest hundreth as needed**
I don't understand what the only one of two bases part means otherwise: 590000=pi*r^2*h+1/2(4/3*pi*r^3)=3.1415... Cost=2pi*r+2(1/2(4*pi*r^2)=6.2831853rh... Solve the first equation for h: h=(590000-2.0943951r^3)/(3.14159r^2) Substitute h into the 2nd equation: Cost= 6.2831853r(590000-2.0943951r^3)/(3.14159... Solve for minimum value of cost: r=41.30
