1. FINDING THE HEIGHT OF A CONE 15 Minute Math Labs

2. Finding the Height of a Cone Purpose: Find the height of a cone of which an ordinary party cup is a section.

3. Finding the Height of a Cone Purpose: Find the height of a cone of which an ordinary party cup is a section.

4. Finding the Height of a Cone Purpose: Find the height of a cone of which an ordinary party cup is a section. Math principles: Similar triangles, ratios, solving a linear equation, reading a ruler

5. Finding the Height of a Cone

6. Looking at the big picture: Shown here with extended lines is the cone for which we are to find the height (depicted here with a question mark).

7. Finding the Height of a Cone Looking at the big picture: Shown here with extended lines is the cone for which we are to find the height (depicted here with a question mark). The dimensions D 1, D 2, and H 1 will ultimately be applied to the sides of two similar triangles from which the final calculations will be made. However, we must first obtain these measurements as follows:

8. Finding the Height of a Cone

9. Measure small diameter With the cup turned upside down, measure the small inside diameter (D 1 ) of the cup. The actual measurement is marked with an arrow on the ruler in this picture.

10. Finding the Height of a Cone

11. Measure large diameter Next, with the cup upright, measure the large inside diameter (D 2 ).Notice the cup is flared slightly at the top, so reduce the inside diameter by.2cm.

12. Finding the Height of a Cone

13. Measure the height Finally, measure the height of the cup (H 1 ). Be sure to measure all the way to the top.

14. Finding the Height of a Cone The three measurements should be close to the following values D 1 = 5.3 cm D 2 = 8.5 cm H 1 = 7.0 cm

15. Finding the Height of a Cone

16. Final calculation: From the two similar triangles, set up a proportion

17. Finding the Height of a Cone Final calculation: From the two similar triangles, set up a proportion

18. Finding the Height of a Cone Final calculation: From the two similar triangles, set up a proportion Cross multiply, substitute in the values obtained for D 1, D 2, and H 1 and get:.5(8.5)X =.5(5.3)(7+X)

19. Finding the Height of a Cone Final calculation: From the two similar triangles, set up a proportion Cross multiply, substitute in the values obtained for D 1, D 2, and H 1 and get:.5(8.5)X =.5(5.3)(7+X) Solve for x and get X = 11.59

20. Finding the Height of a Cone Final calculation: From the two similar triangles, set up a proportion Cross multiply, substitute in the values obtained for D 1, D 2, and H 1 and get:.5(8.5)X =.5(5.3)(7+X) Solve for x and get X = 11.59 Height of the cone = X + H 1

21. Finding the Height of a Cone Final calculation: From the two similar triangles, set up a proportion Cross multiply, substitute in the values obtained for D 1, D 2, and H 1 and get:.5(8.5)X =.5(5.3)(7+X) Solve for x and get X = 11.59 Height of the cone = X + H 1 = 11.59 + 7

22. Finding the Height of a Cone Final calculation: From the two similar triangles, set up a proportion Cross multiply, substitute in the values obtained for D 1, D 2, and H 1 and get:.5(8.5)X =.5(5.3)(7+X) Solve for x and get X = 11.59 Height of the cone = X + H 1 = 11.59 + 7 = 18.59 cm

23. FINDING THE HEIGHT OF A CONE 15 Minute Math Labs