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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
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Best Answer 

 #1
avatar+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: 

3+0 Answers

 #1
avatar+18 
+2
Best Answer

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
avatar+281 
0

The correct answer is actually 36sqrt2.

 
michaelcai  Oct 10, 2017
 #3
avatar+327 
0

Let's make your answer a bit clearer.

\(36\sqrt{2}\)

 
AdamTaurus  Oct 10, 2017

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