My PBL Page: Giant Sphere

Introduction:

My project is a giant sphere made of plastic cups. The significance of the cups is that they are used to find the surface area of the sphere. This is done by stapling all of the cups together in a way that they make a sphere. The surface area varies to how many cups you use. By measuring the diameter of the opening of one cup, you can use them as a form of measurement. By aligning the cups from one point of the sphere to another, you can find the diameter, divide it by 2 and find the radius. Then you just use the surface area for spheres which is, A = 4 x Pi x R^2.

Driving question:

How would you calculate the surface are of sphere? What's the relation between area and radius?

The formula of the surface area of the sphere 4 x Pi x r^2. Where r is the radius of the sphere. This formula was discovered over two thousand years ago by the Greek philosopher Archimedes. He also realized that the surface area of a sphere is exactly equal to the area of the curved wall of its circumscribed cylinder, which is the smallest cylinder that can contain the sphere. Similarity: I've used similarity to calculate and compare the surface are of inside and out side of giant sphere. There are 2 spheres when you complete the giant sphere design. Surface Areas' ratio is equal to radius' ratios square.

Materials:

  • Plastic cups

  • Staplers

  • Staples

Procedure:

Staple 22/23 cups side by side for the first layer, then for the second layer you staple 2 less than the previous layer and repeat that until the half sphere comes to a close.

  • Ring 1: Staple enough cups to make a nice tidy flat circle.

  • Ring 2-3 cups smaller than Ring 1. Continue making smaller and smaller rings until you have enough for one side. Each ring will be 2-5 cups smaller than the one before

  • Half of the giant sphere

When sides are done, fit together and create your own giant sphere.

PBL INVESTIGATION

1. What kind of geometric principals are applied to the Giant Sphere PBL?

Math/Geometry Component:

Spheres are used in geometry, more specifically, spherical geometry. In Euclidean plane geometry, the sphere's points are defined in usual sense. In spherical trigonometry, the angles are defined between great circles. The sum of interior angles of a spherical triangle exceeds 180 degrees.

The formula of the surface area of the sphere 4 x Pi x r^2. Where r is the radius of the sphere. This formula was discovered over two thousand years ago by the Greek philosopher Archimedes. He also realized that the surface area of a sphere is exactly equal to the area of the curved wall of its circumscribed cylinder, which is the smallest cylinder that can contain the sphere.

The formula of the volume of the sphere (4/3) x Pi x r^3.

While outside mathematics the terms "sphere" and "ball" are sometimes used interchangeably, in mathematics a distinction is made between the sphere (a two-dimensional closed surface embedded in three-dimensional Euclidean space) and the ball (a three-dimensional shape that includes the sphere as well as everything inside the sphere.

Similarity: I've used similarity to calculate and compare the surface are of inside and out side of giant sphere. There are 2 spheres when you complete the giant sphere design. Surface Areas' ratio is equal to radius' ratios square.

If you know the surface area

By rearranging the above formula you can find the radius:

r

=

√

a

4

π

where a is the surface area.

2. What's the real life connection about Giant Sphere?

Real Life Connection and Interesting Facts

  1. For a given volume, the sphere is the shape that has the smallest surface area. This why it appears in nature so much, such as water drops, bubbles and planets.

  2. The surface area of a sphere is exactly four times the area of a circle with the same radius. You can see this in the area formula, since the area of a circle is

    1. and the surface area of a sphere is

        1. π

          1. 4

            1. r

            1. ^2

          1. π

              1. r^

              1. 2

People use spheres in everyday life. Most sports use spheres to be able to be played such as basketball, soccer, golf, baseball, and tennis.

  • Hamster owners also use spheres to keep their pets in so they won't get lost easily.

Surface Areas' ratio is equal to radius' ratios square.

4. How many cups did you use to create your sphere? Is there any specific rule to decide number of cups will be used?

I used a total of 80 cups in order to complete my sphere. There is a specific rule to decide number of cups will be used. The rule is 23 – 20 – 17 – 12 – 7 – 1. The first time I tried to make the sphere without following the rule, the shape was more of a cylinder rather than a sphere. This happened countless times and I had to start over until I followed the rule and got it right.

    • Reference: http://thehamsterhouse.com/hamster-care/hamster-exercise/choosing-hamster-ball/

The Earth on which we live on is also a sphere.

3. What would happen to the surface area if the radius decreases or increases? Show your work to calculate small and big sphere's surface area and compare them? Use π = 3.14. Round your answer nearest whole number for radius.

Depending on what the radius is, the surface area will change. If the radius increases then the surface area increases as well. If the radius decreases, so will the surface area. The change will be the (radius)^2.