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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 40. Find the volume of the rectangular prism.

 Jan 30, 2020
 #1
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The volume is 48.

 Jan 30, 2020
 #2
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sorry, could you explain how you got the answer? I'd like to be sure i understand how to solve the problem.

Guest Jan 30, 2020
 #3
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You can assign variables to the side lengths, and then solve the equations.

Guest Jan 30, 2020
 #4
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Well, what I did while checking your answer was

x*y=6

x*z=15

y*z=40

x*y*z=48

48/6=8=z

15/8=1.875

6/1.875= 3.2

3.2*8=25.6, which is wrong.

Guest Jan 30, 2020
 #5
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To make the equations easier to solve, I let

QU = a

UT = b

QR = c.

Then:  area(PQRS) = b·c = 6

           area(PQUT) = a·b = 15

           area(QUVR) = a·c = 40

 

Since b·c = 6     --->   c = 6/b

Since a·c = 40   --->   a = 40/c   --->   a = 40/(6/b)   --->   a = 40·b/6         [substituting]

Since a·b = 15   --->   (40·b/6)·b = 15   --->   40·b2 = 90   --->   b2 = 9/4   --->   b = 3/2

 

Since b = 3/2   --->   b·c = 6   --->   (3/2)·c = 6   --->   c = 4

Since a·c = 40   --->   a·(4) = 40   --->   a = 10

 

The volume of the object = length·width·height = a·b·c  =  (10)·(3/2)·(4)  =  your answer

 Jan 30, 2020

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