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Let PQRSTUVW be a rectangular prism, as shown. The area of face PQRS is 6. The area of face PQUT is 15. The area of face QUVR is 10. Find the volume of the rectangular prism.

 

 Jan 5, 2021
 #1
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Area of  base =   QP * QR   = 6       (1)

 

Area of one side  POUT  = QP * QU   = 15   ⇒   QP =  15/QU     (2)

 

Area of the other side  QUVR  =   QU * QR  =  10  ⇒  QR =  10/QU    (3)

 

Sub (2) , (3) into (1)

 

15/ QU  *  10/QU  =  6

 

150 / QU^2  =   6      rearrange  as

 

QU^2  =  150/6

 

QU^2 =  25          take the square root  

 

QU   =   5

 

So  QP   =  15/5   =  3

And QR =   10/5  =  2

 

So....the volume is   QU  * QP * QR   =   5 * 3   *  2    =     30  units^3

 

 

cool cool cool

 Jan 5, 2021

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