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

michaelcai
Oct 10, 2017

#1**+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

edited by Guest Oct 10, 2017

edited by Guest Oct 10, 2017

#1**+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

edited by Guest Oct 10, 2017

edited by Guest Oct 10, 2017