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Question
There is a ratio 1: 4 between the surface area of two spheres, find the ratio between their radius.
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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