You have 500cm2 of material available to cover different shapes. What is the maximum volume of each object that you can make with this amount of material?
a) a cube
b) a sphere
+6251 What you want to do here is use the fact that the surface area is 500cm2 to solve for the length of a side of the cube or the radius of the sphere.
Then given those you can find the volume of each.
\(\mbox{A cube has surface area }SA=6s^2 \mbox{where }s \mbox{ is the length of a side.} \\ \mbox{It has volume }V=s^3 \\ \mbox{ }\\ \mbox{A sphere has surface area }SA=4\pi r^2 \\ \mbox{It has volume }V=\dfrac 4 3 \pi r^3\)
+6251 What you want to do here is use the fact that the surface area is 500cm2 to solve for the length of a side of the cube or the radius of the sphere.
Then given those you can find the volume of each.
\(\mbox{A cube has surface area }SA=6s^2 \mbox{where }s \mbox{ is the length of a side.} \\ \mbox{It has volume }V=s^3 \\ \mbox{ }\\ \mbox{A sphere has surface area }SA=4\pi r^2 \\ \mbox{It has volume }V=\dfrac 4 3 \pi r^3\)
