#### Pop Quiz 3: Volume of irregular shapes

**Calculate.**

**How big is that Rock?**

Measuring volume of regular shapes involves the straightforward application of formulas. However, when it comes to finding the volume of irregular shapes, like rocks, we have to employ more clever methods. One way of figuring out volume is to measure how much water an object displaces. If you don’t mind making a bit of mess, this is a fun experiment to perform at home. Hint, you can use it on regular shapes as well, and then have your kids check their work!

Below is a picture of a square water tank with dimensions 6 cm by 6 cm by 4 cm. In the first picture the water tank is partially filled with water (2 cm of water). After the rock is put into the tank, the water level rises to 3 cm. Calculate how much water was displaced to find the volume of the rock.

For the answer to this Pop Quiz, we even received a photo of the kids helping with the measurement. I suppose we won’t consider that cheating… this time.

Here’s the answer, sent in by Kelly. Thanks Kelly!

The way to figure out the volume of the rock is to first figure out the volume of the water that’s displaced by the rock.

First: Figure out the volume of the water in the take without the rock in it.

Volume = side x side x side –so–

Volume (before rock) = 6cm x 6cm x 2cm

which = 72cm³

Second: Then you have to add the rock and calculate the new volume with the rock added

Volume (after rock) = 6cm x 6cm x 3cm

which = 108cm³

Last Step: You find the volume of the rock by subtracting the volume of the water before the rock from the volume of the water after you’ve added the rock.

Volume (with the rock) – Volume (before the rock) = Volume (of the rock)

108cm³ – 72cm³ = 36cm³

**Answer: **36cm³

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