Cylinder and Cone Experiment

Cylinder and Cone with Rice

Class was fun today! We discussed formulas for a right prism, pyramid, cylinder, cone, and sphere.  The two that I chose are the cylinder and the cone.  The equation for the cylinder is

V

=

π

r

2

h  

and the cone is 

V

=

π

r

2

h

3

The purpose of this activity was to develop the relationship between the volume of a cylinder and its related cone. First, we compared the bases and heights of each one and how they relate to each other which was that they were identical in base and height.  Then, we had to estimate how many of the cones would fill the cylinder up with rice.  My group guessed that two cones of the rice would fill up the cylinder and we were wrong.  The correct answer was that three cones would fill up the cylinder with rice.  After that, we had to write a ratio that compared the volume of the cone to the volume of the cylinder which was 3:1.  The last step was to write a rule or formula to determine the volume of a cone based on the formula for the volume of a cylinder which we wrote as :V=πr2h/3.     

Sources:

Cylinder with cone and rice, Mesa Community College. Personal photograph by Miranda Tachine-Benally. 2016.

Tachine-Benally, Miranda. Chapter 13- Concepts of Measurement. 03 Oct. 2016. Pyramids and Cone Worksheet. Mesa Community College. Mesa.   

The Scorpion and the Cricket

Figure A

Figure B

 I honestly had a hard time with a problem in class today.  This particular problem was a homework assignment in which we (students) had to figure out the shortest route the scorpion can crawl to get to the cricket.  As you can see in my drawings, I have labeled the scorpion and the cricket.  The scorpion is seated in the center of the right wall, 1 feet from the ceiling.  The cricket is seated in the center of the left wall, 1 feet from the floor.  The dimensions of the rectangular room is labeled as the base being 30 feet (a), the height being 12 feet (b), and the width being 12 feet (Figure A).

In Figure B, I unfolded the rectangle into a net and implemented the Pythagorean theorem.  Then I figured out my new dimensions and labeled them accordingly.  Then, I calculated my figures using the Pythagorean theorem which is a² + b² = c².  As shown in Figure B, the end result was 40 with the conclusion that the shortest route the scorpion can crawl to get to the cricket was 40 feet.

Sources:

Net of a Rectangular Room, Mesa Community College. Personal photograph by Miranda Tachine-Benally. 2016.

Tachine-Benally, Miranda. The Scorpion and the Cricket. 03 Oct. 2016. Classroom Worksheet. Mesa Community College, Mesa.