Sphere 1 has surface area A1and volume V1, and sphere 2 has surface area A2and volume...

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Sphere 1 has surface area A1and volume V1, and sphere 2 has surface area A2and volume...

Sphere 1 has surface area A₁and volume V₁, and sphere 2 has surface area A₂and volume V₂. If the radius of sphere 2 is 9times the radius of sphere 1, what is the ratio of each of the following?

(a) the areas, A₂/A₁

(b) the volumes, V₂/V₁

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Answer 1

Answer #1

area of sphere = 4(pi)r^2

sphere 1: A = 4(pi)r^2

sphere 2: A = 4(pi)(9r)^2

(a) A2 / A1 = 9^2 = 81

(b) By inference of the powers:

V2 / V1 = 9^3 = 729

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Answer 2

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