Question

1. Sphere 1 has surface area A₁ and volume V₁ and sphere 2 has surface area A₂ and volume V₂. If the radius of sphere 2 is 3.86 times the radius of sphere 1, what is the ratio of the areas A₂/A₁?

2. What is the ratio of the volumes V₂/V₁

Answer 1

We know that area of a sphere is given as

A = 4r²

given

r2 = 3.86 * r1

so,

A2 / A1 = r2² / r1²

4 will get cancelled

A2 / A1 = 3.86² * r1² / r1²

A2 / A1 = 14.89

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volume of sphere is given as

V = 4/3r³

4/3 will get cancelled, we get

V2 / V1 = r2³ / r1³

V2/ V1 = 3.86³

V2 / V1 = 57.51