To find the slant height of the square pyramid, we can use the Pythagorean theorem.
Let's first find the length of the diagonal of the square base.
The diameter of the bottom is equal to the diagonal of the square.
The formula to find the diagonal of a square is d = √(2s^2), where d is the diagonal and s is the side length of the square.
In this case, the diameter (d) is 16, so we can find the side length (s) of the square as:
16 = √(2s^2)
16^2 = 2s^2
256 = 2s^2
s^2 = 256/2
s^2 = 128
s = √128
s ≈ 11.31
Therefore, the side length of the square base is approximately 11.31 units.
Now, let's find the slant height of the pyramid.
In a pyramid, the slant height (l) can be found using the Pythagorean theorem, where l is the slant height, s is the side length of the base, and h is the height of the pyramid.
In this case, s ≈ 11.31 and h = 15.
Using the Pythagorean theorem:
l^2 = h^2 + s^2
l^2 = 15^2 + 11.31^2
l^2 = 225 + 128
l^2 = 353
l ≈ √353
l ≈ 18.78
Therefore, the slant height of the square pyramid is approximately 18.78 units.
Find the slant height of the square pyramid.
16 is the diameter of the bottom and from the point down it's 15.
1 answer