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# Each of the eight edges of a regular square pyramid has length 6. Find the volume of the pyramid.

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Each of the eight edges of a regular square pyramid has length 6. Find the volume of the pyramid.

michaelcai  Oct 10, 2017

#1
+18
+2

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

ChowMein  Oct 10, 2017
edited by Guest  Oct 10, 2017
edited by Guest  Oct 10, 2017
edited by Guest  Oct 10, 2017
Sort:

#1
+18
+2

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

ChowMein  Oct 10, 2017
edited by Guest  Oct 10, 2017
edited by Guest  Oct 10, 2017
edited by Guest  Oct 10, 2017
#2
+509
0

The correct answer is actually 36sqrt2.

michaelcai  Oct 10, 2017
#3
+648
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$$36\sqrt{2}$$