Today grade 9s worked through 3 stations to learn about how to use various formulae to calculate surface area and volume of cones, pyramids and spheres. We used a displacement method to show that a sphere will displace enough water to fill a cylinder that has height and diameter equal to the sphere diameter by 2/3.

We can use the fact that the height of the cylinder=2r to modify the formula of the cylinder from V=(pi)(r)^2(h) to V=(pi)(r)^2(2h) to V=2(pi)(r)^3

The sphere’s volume is 2/3 of this or V=(4pir^3)/3 Another station was for calculating the surface area of the sphere. We drew circles with the same radius as the orange. Then we peeled the orange, and filled the circles that we could. We can fill 4 circles, so the formula for the surface area of a sphere is A=4(pi)(r)^2 Other stations were for calculating different aspects of a pyramid. And exploring about cones. We looked at the lateral surface area, and the slant height, and radius and height and verified that the pythagorean theorem works to calculate missing information. Tomorrow we will finish our remaining stations and apply our knowledge to solve problems.