First of all, look at those beans!

And those beans! Wonder what’s different with these ones….

We got to work today in 5 different stations.

For one, we used displacement of water to determine the volume of a sphere.  Juice concentrate containers have the same radius as a tennis ball, so they work nicely.  The container is cut so the height is equal to the diameter.

Water is displaced, and fills the cylinder 2/3 of the way.

The volume of the cylinder is V=(pi)(r^2)(h), but remember h=2r, so the volume is V=(pi)(r^2)(2r) which simplifies to V=2(pi)(r^3)

So the sphere volume is 2/3 of that.

V=(2/3)(2)(pi)(r^3)

V=(4/3)(pi)(r^3)

We also looked at the surface of a sphere.  We drew circles with the same radius as the orange, then peeled the orange and tried to fill up the circles.

We ended up filling 4 circles.  We know the area of a circle is (pi)(r)^2 so the whole sphere is A=4(pi)r^2

We did an activity with the lateral surface of a cone, using a “pacman” made from the centre of a paper plate.  We looked at how slant height is related to the height and the radius using pythagorean theorem (again).

We also explored pyramids in Egypt to determine the area and volume of the great pyramid (in cubits). For this we needed to learn a bit about scientific notation.

We also learned about a pyramid in Mexico in the town of Cobà, which you can climb.  We determined he lengh of “safety rope” that would be needed to run the length of the side.

With 12 minutes per station, we all got to experience every bit, and practice for our upcoming summative.