MATH 1120 The Cone Problem: Application Problem #1 Name(s): ___________________________________________ Overall Goal Given: A cone with a slant height of 10 cm. Find: The relationship between the volume of the cone and the angle . I. Making Conjectures 1a) Sketch the cone with a very small angle , keeping in mind that the slant height is constant. Describe the effect on the radius and height of the cone. b) Sketch the cone with a very large angle , keeping in mind that the slant height is constant. Describe the effect on the radius and height of the cone. c) Make a conjecture regarding which type of angle would create a larger volume. Justify your answer. The formula for the volume of a cone is V = 1 3 r2 h . II. Using Trigonometry to Calculate Radius & Height 2a) Notice a right triangle is formed within the cone by the height and the radius. Use a trig function to write an equation and then solve the equation for r to find the radius of the cone. Radius = _____________________ b) Using the same right triangle, write an equation to find the height of the cone. Height = ____________________ 1 0h r 10 h r 10 r 10 h c) Using the equations for radius and height from section II, use the volume of the cone formula from section I to write an equation to find the volume of the cone in terms of the angle . V = _________________________ III. Collecting Data 3a) Use your volume equation to fill in the table below for each of the given angles . Use a calculator to help you