I am redesigning a rectangular prism in geometry where I have to minimize the surface area while maintaining the same volume. I have to recreate three of these. Now My original prism has a surface area of 122.5in^2 and a volume of 58.75in^3. I want to make my first redesign, a shpere. How would I do that. For my second one, a square pyramid, and the third one a cylinder. How would I recreate these with the same volume, but smaller surface area? The length is 5 inches, the height is 4.7 inches, and the width is 2.5 inches

Question

Mathematics

Ronan Horne

15 February, 09:11

I am redesigning a rectangular prism in geometry where I have to minimize the surface area while maintaining the same volume. I have to recreate three of these. Now My original prism has a surface area of 122.5in^2 and a volume of 58.75in^3. I want to make my first redesign, a shpere. How would I do that. For my second one, a square pyramid, and the third one a cylinder. How would I recreate these with the same volume, but smaller surface area? The length is 5 inches, the height is 4.7 inches, and the width is 2.5 inches

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Kenna Garrett · Answer 1

Think about a really long, flat 3-dimensional object. This has a certain volume, and a certain (big) surface area because of its length. Now, make the 3-dimensional object fat and maintain the volume. Notice how you have minimized surface area but maintained volume. This is how I would go about solving it.