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Math Teaser
Problem
A canning factory is able to produce 4,800 cans of soup in one hour. At this rate, in how many minutes can the canning factory produce 400 cans?
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PSAT: Math Question #7

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Question:
 In the figure above,  P  is the center of a circle with area  9  π   , 
 points  Q  and  R  lie on the circle, and angle  a  is  45  °   . What is the 
 length of  QR?


Choices:
A. 3 2
B. 3
C. 9 2
D. 9
E. 18

The correct answer is (A).

To solve this one, we must first find the radius of the circle.

The correct answer is (A).

To solve this one, we must first find the radius of the circle.

 Knowing the area of the circle is  9  π   , we can find the radius 
 using the formula for the area of a circle: 

A  =   π  r2
9  π   =   π  r2
9  =  r2
3  =  r
a2  +  b2  =  c2
32  +  32  =  QR2
9  +  9  =  QR2
18  =  QR2
18
 =  QR
3
2
 =  QR

Now, we can proceed to the solution in several different ways. One way is to use the Pythagorean theorem:
 

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