# Volume of pyramid

1. Mar 19, 2011

### chawki

1. The problem statement, all variables and given/known data
The volume of a pyramid can be evaluated by using the equation V=1/3*A*h where h is
the height of the pyramid and A is the area of the base of the pyramid. The problem is
to design such a triangular pyramid where the volume is V = 72 cm3 and the height is
h = 12 cm. The base of the pyramid is a rectangular isosceles triangle.

2. Relevant equations
a) Determine the area of the base of the pyramid. Pay attention to the unit of your answer.
b) Draw a picture of the base triangle of the pyramid in a proper scale
3. The attempt at a solution
a)
V=1/3*A*h
A=72/(12/3)=18cm2

b) A = 18 = b*y
b=y
so: 18=2*b => b = 9cm

#### Attached Files:

• ###### Volume of pyramid.JPG
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2. Mar 19, 2011

### LCKurtz

Your picture didn't come through, but I'm guessing your formula A = 18 = b*y is wrong. Remember the area of a triangle is (1/2)base * height. And even if it were correct, b = y wouldn't give you 18 = 2b, it would be 18 = b2. Two things to fix.

3. Mar 20, 2011

### HallsofIvy

Staff Emeritus
Well, I can see your picture and it isn't even of a triangle!

Did you simply misread the problem?

4. Mar 20, 2011

### chawki

Yes i did my mistake, i thought it's a pyramid with 4 faces..

but then we have the area of a triangle that equal 18m2
18=(b*y)/2
To be able to draw that triangle we need to find the length of just one side (assuming the sides are equal) and the problem is..we don't have that

#### Attached Files:

• ###### Volume of pyramid.JPG
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5. Mar 22, 2011

### chawki

some please give me a hint

6. Mar 22, 2011

### LCKurtz

You still haven't drawn a picture of your pyramid. When you do I think you will find what you need in my earlier post. (reply #2).

7. Mar 22, 2011

### chawki

i'm not good in drawing but i have an image of it in my mind..and i can't see how i will find the length of the side of that triangle

8. Mar 22, 2011

### LCKurtz

Earlier you had that V = (1/3)Ah and you are given that V = 72 and h = 12.

So A = 3V/h = 3*72/12 = 18.

You had that a long time ago. So the area of your isosceles "rectangular" triangle is 18. I presume you know what isosceles means and I presume that "rectangular" triangle means what is usually called a right triangle. And as I pointed out in post #2, the area of a triangle is (1/2)*base* height. What exactly are you stuck on, given you have all this information?

9. Mar 22, 2011

### chawki

how you know that the triangle is isosceles ? isn't suppose to be equilateral ?

10. Mar 22, 2011

### LCKurtz

11. Mar 22, 2011

### chawki

ok i must be blind :/
but still we can't find the dimension of that triangle..it's about the triangle and we need the height of the triangle, not the pyramid

12. Mar 22, 2011

### LCKurtz

I asked you before if "rectangular" triangle means right triangle. You didn't answer that, but I assume it does. You have an isosceles right triangle and you know its area is 18. Draw a picture of it. You should be able to figure out its dimensions from the picture.

13. Mar 23, 2011

### chawki

here it is...
i guess that the base of this triangle = it's height.

#### Attached Files:

• ###### Volume of pyramid.JPG
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14. Mar 23, 2011

### HallsofIvy

Staff Emeritus
Yes, and taking "s" to be the length of one of the legs, the area of the base is
$$\frac{1}{2}s^2= 18$$.

15. Mar 23, 2011

### chawki

ahh ok..now i get it..
s2 = 36
s = 6 cm

and then we find the hypotenuse = approximately 8.5 cm

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