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Maximizing Rectangular Prism Volume Versus Surface Area

Directions: What is the greatest volume you can make with a rectangular prism that has a surface area of 20 square units?

Hint

Hint

What shape maximizes volume in relation to surface area in rectangular prisms?

Answer

Answer

A cube has the maximum volume amongst rectangular prisms with the same surface area. So, a cube with a surface area of 20 square units has six sides that each have an area of 10/3 square units. The square root of 10/3 gives us the length of each side.

Source: Robert Kaplinsky

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