gandako 3 years ago suppose the lateral area of a right circular cone and the area of a sphere is equal 64π inches^2. if the radius of the sphere and the radius of the base of the cone are equal, what is the volume of the cone?

1. Miyuru

Is the question complete..? :D

2. gandako

3. Miyuru

|dw:1350220886630:dw|

4. gandako

i really don't know how it looks like,but i guess what you did was right. :)

5. gandako

how can I find the total area and volume?:(

6. experimentX

what's the prism ? what's pyramid? make your figure properly ... this shouldn't be difficult.

7. experimentX

|dw:1350221237912:dw|

8. gandako

regular hexagonal prism with 10-in long sides and apothem of length 9-in long. uhh, yeah! I think so.

9. experimentX

|dw:1350221347921:dw| |dw:1350221367792:dw|

10. Miyuru

|dw:1350221334283:dw|

11. gandako

miyuri what is 12 there?

12. gandako

experimentX yeah but how can i find the volume and total area?

13. Miyuru

It would be essential in finding the volume...

14. Miyuru

To find the total area multiply the area of triangle by 6 + area of hexagon..

15. experimentX

volume of pyramid = 1/3* area of hexagon * height

16. experimentX

for surface area ... |dw:1350221785183:dw|

17. experimentX

|dw:1350221947122:dw|

18. Miyuru

Total area = $(\frac{15*10}{2}*6)+(\frac{10*9}{2}*6)$

19. experimentX

yeah ... looks like that's correct!!

20. gandako

Gee! thanks a lot!!!!! but how is this? find the volume of the region outside the pyramid and inside the prism.

21. experimentX

find the volume of pyramid ... find the volume of prism ... subtract 1 from 2

22. Miyuru

Volume = $(\frac{10*9}{2}*6)*\frac{1}{3}*12 - (\frac{10*9}{2}*6*12)$

23. experimentX

lol ... you did the opposite? is height 12??

24. Miyuru

I took the height of the pyramid...

25. experimentX

should be something like this if 12 is height $- (\frac{10*9}{2}*6)*\frac{1}{3}*12 + (\frac{10*9}{2}*6*12)$

26. Miyuru

Oops yeah @experimentX I changed the sides of the equation... :D

27. experimentX

well ...i guess that it is!!

28. gandako

so 4320 is the volume?=)

29. gandako

What is the area of the base and the height?

30. Miyuru

Yeah @gandako U are correct.. volume=4320

31. Miyuru

I found the height from the triangle drawn above.. x=12

32. gandako

but how about the are of the base @Miyuru ?

33. Miyuru

Base = side of the hexagon

34. gandako

i can't understand:(

35. Miyuru

From which step are you confused?

36. gandako

here: volume of pyramid=1/3 * area of the base *height how can get the are of the base?

37. Miyuru

Here the base is the hexagon and it's area is six times the area of a triangle...

38. gandako

6 x bh/2 is this? what is the value of b in there?

39. Miyuru

b = 10