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A right pyramid has a square base with area 288 square cm. Its peak is 15 cm from each of the other vertices. What is the volume of the pyramid, in cubic centimeters?

tertre  Mar 18, 2018

Best Answer 

 #2
avatar+7339 
+2

I also get  864  cm3  (but exactly)  smiley

 

 

area of square base  =  288    so   side length of base  =  √288

 

Let  x  be the diagonal of the base.

Let  h  be the height of the pyramid.

 

By the Pythagorean theorem....

(√288)2 + (√288)2   =   x2

288 + 288   =   x2

576   =   x2

x   =   √576

x   =   24

 

Again by the Pythagorean theorem...

(x/2)2 + h2  =  152

(24/2)2 + h2  =  152

144 + h2  =  225

h2  =  81

h   =   9

 

volume of pyramid   =   (1/3)(area of base)(height)

volume of pyramid   =   (1/3)(288)(9)

volume of pyramid   =   864      cm3

hectictar  Mar 19, 2018
 #1
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+1

OK, I will take a crack at it! Let me know if I s***w up!!

 

Sqrt(288) = 16.97 cm - side length of the square base 

By Pythagoras' theorem:

Slant Height =sqrt[15^2 - (16.97/2)^2]

Slant Height =12.3695 cm

Height =sqrt[12.3695^2 - 8.485^2]

Height =9 cm

Volume = 1/3 x H x Side Length^2

Volume = 1/3 x 9 x 16.97^2

Volume =~864 cm^3

Guest Mar 19, 2018
 #2
avatar+7339 
+2
Best Answer

I also get  864  cm3  (but exactly)  smiley

 

 

area of square base  =  288    so   side length of base  =  √288

 

Let  x  be the diagonal of the base.

Let  h  be the height of the pyramid.

 

By the Pythagorean theorem....

(√288)2 + (√288)2   =   x2

288 + 288   =   x2

576   =   x2

x   =   √576

x   =   24

 

Again by the Pythagorean theorem...

(x/2)2 + h2  =  152

(24/2)2 + h2  =  152

144 + h2  =  225

h2  =  81

h   =   9

 

volume of pyramid   =   (1/3)(area of base)(height)

volume of pyramid   =   (1/3)(288)(9)

volume of pyramid   =   864      cm3

hectictar  Mar 19, 2018

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