anonymous 4 years ago Using integrals, how do you find the volume of a equilateral triangle based pyramid with height h? let a equal one side of the triangular base

1. slaaibak

Ha, good question. Hmm, I think it would be best to define a pyramid in terms of planes, and then using rectangular coordinates to solve

2. anonymous

|dw:1354836422356:dw|

3. anonymous

@Algebraic! hey Chief, can you help me out with this volume problem?

4. anonymous

|dw:1354836727530:dw|

5. slaaibak
6. anonymous

How does he get A=root(3)/2 (a^2)

7. slaaibak

|dw:1354837670054:dw|

8. slaaibak

That's using pythagoras. Then the area is just A=bh/2

9. slaaibak

hmm weird, i'd get A=root(3)/4 (a^2)

10. anonymous

Huh. That is weird. That's what I got also.

11. slaaibak

he made a mistake it seems. $A = {\sqrt 3 \over 4} \times a^2$

12. anonymous

Would that mean this his equation for S(r) is wrong also?

13. slaaibak

I think S(r) is correct.