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The ratios of areas of two spheres is 1:4. Find the radius of larger one if the small...

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christiano-cr7 | Salutatorian

Posted July 4, 2013 at 10:01 AM via web

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The ratios of areas of two spheres is 1:4. Find the radius of larger one if the small one has 5cm radius.

 

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 4, 2013 at 10:09 AM (Answer #1)

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Area of a sphere is given by;

`A = 4pir^2`

Let us say the area of the large sphere is rcm.

`A_L = 4pir^2 ---(1)`

`A_M = 4pi(5)^2 -----(2)`

 

(1)/(2)

`A_L/A_M = r^2/25`

`4/1 = r^2/25`

`r^2 = 100`

`r = 10`

 

So the radius of the larger sphere is 10cm.

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