Teacher Guide, Geometry Activity 1

TEKS addressed: (G.7)(A); (G.8)(A); (G.8)(D); (G.11)(B); (G.11)(C)

This is a good Pre-AP* worksheet because it builds upon and extends skills that students have developed in middle school and Algebra I (using geometric formulas, solving literal equations, symbolic manipulation, function notation) while simultaneously addressing the TEKS listed above for high school geometry. It does so in a way very different from that seen in most textbooks. Most importantly, the context and wording is based upon an actual AP problem with which the students had difficulty.

1. Write an expression for the area of a circle as a function of its circumference.

2. Write an expression for the perimeter of a square as a function of its area.

3. If the volume of a right circular cylinder is 400π cubic units, write an expression for its lateral surface area as a function of its radius.

4. Water is being stored in a conical tank with height 12 feet and base diameter 8 feet. Write an expression for the volume of water in the conical tank as a function of h, the height of the water in the tank.

5. Water is being stored in a cylindrical tank that has a base with area 900π square feet. Write an expression for the volume of water in the cylindrical tank as a function of h, the height of the water in the tank.

6. Write an expression for the area of an equilateral triangle as a function of the length of one of its sides.

7. Write an expression for the area of a circle as a function of its diameter.

8. Write an expression for the surface area of a sphere as a function of its volume.

9. Write an expression for the volume of a cube as a function of its surface area.

10. If the area of the base of a cone is 25π square units, express the volume of the cone as a function of its height.