- #1
doctordiddy
- 54
- 0
Homework Statement
Find the volume of a pyramid with height 24 and with base an equilateral triangle with side 11.
Homework Equations
The Attempt at a Solution
So I know the relationship
h/x=b/l
where h is my height 24
x is simply x or height above base
b is my base 11
l is the length of the base at height x
i also know the integral is
∫024(A(x))dx
I am having trouble finding A(x)
I believe that it you would use the area of the equilateral triangle
so i know area of the triangle is base*height/2
I also know that base is l, and height is unknown, but i do know that
l^2=(l/2)^2 + z^2 where i take z as the height of the equilateral triangle
then z= √(l^2 -(l/2)^2 )
so area of the triangle would finall be
[(l^2)√(l^2 - (l/2)^2)]/2
I would finally plug in l=bx/h from the identity h/x=b/l
However, when i do this, i end up with an integral i am unable to solve. I feel like there is another way to do this, can anyone help?
edit: I mean an easier way using integrals, not volume of a pyramid please
thanks