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Same volume, different areas.

October 1, 2019

Grade 9s were tasked with creating rectangular prisms today with volumes that were 300cm^3.

Many groups made plans first, then measured and cut out their boxes.

Each group had to then calculate the surface area of their prism.

And then were tasked with making another one, with the same volume and a bigger or smaller area.

After all of the prisms were made, we arranged them from smallest to biggest surface area.

We now know that if the volume is the same for two prisms, the surface area is not always going to be the same. The surface area can be bigger or smaller in number than the volume.

We noticed that the closer the dimensions get to being the same, the smaller the surface area gets (a cube is always the least area), and when the dimensions get really different (plate or snake shapes) the area gets big.

Applications of this are when we package objects, we aim for the most cube shaped box, to save money (less material needed for the box). We also can find this surface area/volume ratio in biology, as the reason for cell division, why we have dense spongy lungs, and why worms can breathe through their skin.

Good work today grade 9s!

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