+619 Each of the eight edges of a regular square pyramid has length 6. Find the volume of the pyramid.
+154 We need to find the base first.
b=l*w
b=6*6
b=36
Next, we need to find the slant height.
Find s using the pythagorean theorem,
s^2=6^2-3^2
s=√36-9
s=√27=3√3
Great, now we have s. The only thing that's left is h, for the formula for the volume of a pyramid.
V=bh/3
We need h. To help you better visualize the picture above, take a look at this one.
Since the sides are 6, r is side/2 = 3.
Use pythagorean theorem for h.
h=√(3√3)²-3²
h=√27-9
h=√18
Alright, lets plug everything into the volume formula.
V=bh/3
V=36√18/3
V=36√9*2/3
V=108√2/3
V=36√2=50.9 units^3
+154 We need to find the base first.
b=l*w
b=6*6
b=36
Next, we need to find the slant height.
Find s using the pythagorean theorem,
s^2=6^2-3^2
s=√36-9
s=√27=3√3
Great, now we have s. The only thing that's left is h, for the formula for the volume of a pyramid.
V=bh/3
We need h. To help you better visualize the picture above, take a look at this one.
Since the sides are 6, r is side/2 = 3.
Use pythagorean theorem for h.
h=√(3√3)²-3²
h=√27-9
h=√18
Alright, lets plug everything into the volume formula.
V=bh/3
V=36√18/3
V=36√9*2/3
V=108√2/3
V=36√2=50.9 units^3
