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Question
There is a ratio 1: 4 between the surface area of two spheres, find the ratio between their radius.
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Solution
Let radius of spheres are r1 and r2.
So, surface area of spheres is 4πr12 and 4πr22.
Ratio of surface area = `(4πr_1^2)/(4πr_2^2) = 1/4`
= `(r_1^2)/(r_2^2) = 1/4`
= `((r_1)/(r_2))^2 = 1/4`
= `(r_1)/(r_2) = sqrt(1/4)`
= `(r_1)/(r_2) = 1/2`
Hence, the ratio between their radius = 1: 2.
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