Question

How do you find the Volume for a pyramid with 3 sides that all equal 8 m, the height equals 11 m and the slant height 11.2 m

Answer 1

@acehuert

Answer 2

thats kinda confusing

Answer 3

61.6

Answer 4

Don't give direct answers. :)

Answer 5

It won't help them solve the problem in the meer future, so please don't give direct answers, try and help them out a bit.

Answer 6

Still doesn't help when people give you direct answers. (:

Answer 7

Volume of a pyramid is given by \[
\text{Volume} = \frac13\cdot\text{base area}\cdot \text{height}
\]We know that
\[
\text{height} = 11m
\]
For the base area, we need to use the area of a triangle: \[
\text{Area} = \frac12\cdot\text{base}\cdot \text{height}
\]Note this is the triangle height, not the pyramid height.
The triangle base is 8m.

We can observe the following to get the height of an equilateral triangle.

Using the pythogorean theorem: \[
h^2+(s/2)^2 = s^2 \implies h^2= s^2 - (s/2)^2 = 3s^2/4 \implies h = (\sqrt{3}/2)s
\]
Thus the area of an equilateral triangle is: \[
A = \frac12 \cdot \frac{\sqrt 3}{2}s\cdot s = \frac{\sqrt3}{4}s^2
\]
Finally, we plug this all back into our initial equation to get: \[
V = \frac13 \cdot \frac{\sqrt 3}{4} \cdot (8m)^2 \cdot 11 m = \frac{176\sqrt 3}{3}m^3 \approx 101.6 m^3
\]
My main concern is that I'm not sure what the purpose of providing the slant height was. Perhaps there is a formula which uses the slant height that makes it easier to find the volume, but I'm not currently aware of one.

Answer 8

nerd