I have enough pure silver to coat $$ 3 $$ square meters of surface area. I plan to coat a sphere and a cube. Allowing for the possibility of all the silver going onto one of the solids, what dimensions should they be if the total volume of the silvered solids is to be a maximum? The radius of the sphere is $$\square $$ meters, and the length of the sides of the cube is $$ \square $$ meters. Again, allowing for the possibility of all the silver going onto one of the solids, what dimensions should they be if the total volume of the silvered solids is to be a minimum? The radius of the sphere is $$ \square m ,$$ and the length of the sides of the cube is $$ \square m $$ .

Question

I have enough pure silver to coat $$ 3 $$ square meters of surface area. I plan to coat a sphere and a cube. Allowing for the possibility of all the silver going onto one of the solids, what dimensions should they be if the total volume of the silvered solids is to be a maximum? The radius of the sphere is $$\square $$  meters, and the length of the sides of the cube is $$ \square $$ meters. Again, allowing for the possibility of all the silver going onto one of the solids, what dimensions should they be if the total volume of the silvered solids is to be a minimum? The radius of the sphere is $$ \square m ,$$ and the length of the sides of the cube is $$ \square m $$ .

Pollard Boone · Accepted Answer

Radius = 0.4873 mLength of sides = 0.052 mRadius = 0.4886 mLength of the sides of the cube is 0.7071 m

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