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natita [175]
3 years ago
6

Sphere 1 has surface area A₁ and volume V₁, sphere 2 has surface area A₂ and volume V₂. If the radius of sphere 2 is six times t

he radius of sphere 1, what is the ratio \frac{A2}{A1} of the areas? What is the ratio \frac{V2}{V1} of the volumes?
Physics
1 answer:
Sveta_85 [38]3 years ago
8 0

Let , radius of sphere 1 is r .

So , radius of sphere 2 is 6r .

Surface area of sphere is given by :

A=4\pi r^2

So ,

\dfrac{A_2}{A_1}=\dfrac{4\pi(6r)^2}{4\pi r^2}\\\\\dfrac{A_2}{A_1}=36

Volume is given by :

V=\dfrac{4}{3}\pi r^3

Ratio of sphere 2 by sphere 1 is given by :

\dfrac{V_2}{V_1}=\dfrac{\dfrac{4}{3}\pi (6r)^3}{\dfrac{4}{3}\pi r^3}\\\\\dfrac{V_2}{V_1}=216

Therefore ,  the ratio of area and volume is 36 and 216 respectively .

Hence , this is the required solution .

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