Sphere Day!

Today we calculated the surface area and the volume of spheres.

We explored the volume with a displacement tank. A tennis ball just happens to fit perfectly in a juice concentrate can, so I made a cylinder that is perfectly suited for the tennis ball by cutting the cylinder down so the height of the can is the same as the height of the ball.

We put the tennis ball into the displacement tank and had to press it down since it floats. We caught the displaced water in the cylinder. It filled it 2/3 of the way.

To prove that it was filled 2/3 of the way, we used the cone and sphere from the solids set.

We saw that half a sphere has the same volume as a cone. We already know that a cone has the same volume as 1/3 of the cylinder, so a whole sphere (2 cones worth) is 2/3 of the cylinder.

We went through the derivation using some intense algebra and substitution. We needed to substitute thar h=2r, and then we could get the formula for volume of a sphere.

Surface area was next on the list. We used oranges to help us, since they can be peeled. The peel is the surface of the sphere. We drew circles with the same diameter as the orange, then we peeled the orange and fit the peels into the circles.

We can fill 4 circles perfectly with the peels. This corresponds to the formula of the sphere’s area.

This was our last new learning, and we’ll be preparing for our exams which take place next week.