1. Do Now: Express the area, A, of an equilateral triangle as a function of its sides.

2. What is the relationship between the radius of the base and the height of a cone?
Let’s observe some things that are true about this diagram:
Congruent Triangles:
height
Similar Triangles:
As a result, we may set up the following proportion:
Ex) A water tank has the shape of a right circular cone with its vertex pointing down. The radius, r, of the top is 2 ft and the height, h, of the tank is 8 ft. Express the volume of the water in the tank as a function of its depth.

3. PRIMARY
SECONDARY
Write the radius in terms of h and substitute that radius into the volume equation to get the volume equation in terms of h as well.
Ex) A water tank has the shape of a right circular cone with its vertex pointing down. The radius, r, of the top is 2 ft and the height, h, of the tank is 8 ft. Express the volume of the water in the tank as a function of its depth (height).

4. Functions Worksheet #4-6
4. A water tank has the shape of a right circular cone with its vertex pointing downward. The radius of the top is 3 ft., and the height of the tank is 12 ft. Express the volume of the water in the tank as a function of its depth.

5. 5. The vertical cross sections of a conical water tank are isosceles right triangles. Express the volume of the water in the tank as a function of its depth.
Vertical Cross Sections: A vertical slicing of a cone creating 2 isos. right triangles.
The vertical cross sections of a cone are the triangles that are formed when you slice a cone vertical starting from the tip of the vertex; when you open the cone and look at it head-on you see, in this case, 2 Isosceles right triangles.
PRIMARY
SECONDARY

6. 6. The vertical cross sections of a conical water tank are equilateral triangles. Express the volume of the water in the tank as a function of its depth.
Vertical Cross Sections: A vertical slicing of a cone creating 2 equilateral triangles.
PRIMARY
SECONDARY

7. FINISH WORKSHEET: #7, 8, 9

8. A rectangle is bounded by the x-axis and the semi-circle
REIVEW OF FUNCTION APPS:
A rectangle is bounded by the x-axis and the semi-circle
A Write the area of the rectangle as a function of x and determine the domain of the function.
What if the question said that the rectangle is inscribed in the entire circle?