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A right pyramid has a square base with area 288 square cm. Its peak is \(18\) cm from each of the other vertices. What is the volume of the pyramid, in cubic centimeters?

 Apr 13, 2022
 #1
avatar+55 
-1

1287.975

 Apr 13, 2022
 #2
avatar+122390 
+1

Let's go through this

 

Slant height  =18

 

The side of the base =  sqrt (288)  =  12sqrt 2

 

The diagonal  length of the base  = 12sqrt (2)  * sqrt (2)  =  24

 

Half of this diagonal length  =  12

 

Using the Pythagorean Theorem, the  height of the pyramid  =  sqrt  [  slant height ^2  - (half of diagonal length)^2 ]   = 

 

sqrt [ 18^2 - 12^2 ] =  sqrt (180)  =6 sqrt (5)

 

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

 

(1/3) (288) (6 sqrt (5) )  =

 

2 * 288 * sqrt (5)  =

 

576sqrt (5) cm^3  ≈  1287.975 cm^3    (just as qjin27 found  !!!! )

 Apr 13, 2022

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