the Steradian (Sr) equivalent

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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) Ï€^2/36 Sr
(B) Ï€^2/25 Sr
(C) Ï€^2/16 Sr
(D) Ï€^2/9 Sr
(E) Ï€^2/4 Sr

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

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) Ï€^2/36 Sr
(B) Ï€^2/25 Sr
(C) Ï€^2/16 Sr
(D) Ï€^2/9 Sr
(E) Ï€^2/4 Sr

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

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