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the Steradian (Sr) equivalent

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the Steradian (Sr) equivalent

by sanju09 » Fri Aug 29, 2014 10:06 pm
If a Steradian (Sr) is equal to (180/Ï€) ^2 square degrees, what is the Steradian (Sr) equivalent of 2025 square degrees?
(A) π^2/36 Sr
(B) π^2/25 Sr
(C) π^2/16 Sr
(D) π^2/9 Sr
(E) π^2/4 Sr


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by GMATinsight » Sat Aug 30, 2014 3:30 am
sanju09 wrote:If a Steradian (Sr) is equal to (180/Ï€) ^2 square degrees, what is the Steradian (Sr) equivalent of 2025 square degrees?
(A) π^2/36 Sr
(B) π^2/25 Sr
(C) π^2/16 Sr
(D) π^2/9 Sr
(E) π^2/4 Sr
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by Brent@GMATPrepNow » Sat Aug 30, 2014 11:08 am
sanju09 wrote:If a Steradian (Sr) is equal to (180/π)² square degrees, what is the Steradian (Sr) equivalent of 2025 square degrees?
(A) π²/36 Sr
(B) π²/25 Sr
(C) π²/16 Sr
(D) π²/9 Sr
(E) π²/4 Sr
We can also solve using EQUIVALENT RATIOS.

For every 1 Steradian, there are (180/π)² square degrees
Also, for x Steradians, there are 2025 square degrees
We must find the value of x

So, 1/(180/π)² = x/2025
Multiply both sides by 2025 to get: 2025/(180/π)² = x
Simplify: (π²)(2025)/(180²)
ASIDE: 2025 = 45²
So, we get: (π²)(45²)/(180²)
Rewrite as: (π²)(45/180)²
Simplify: (π²)(1/4)²
Simplify: π²/16

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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